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JEE-Main - Grade 12 - Mathematics - Integrals - Introduction and Snapshot of Integrals - Study ref# 917
Introduction Differential Calculus is centered on the concept of the derivative. The original motivation for the derivative was the problem of defining tangent lines to the graphs of functions and calculating the slope of such lines. Inte...
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JEE-Main - Grade 12 - Mathematics - Integrals - Introduction and Snapshot of Integrals - Study ref# 918
Following sections must be covered to understand the Integrals: 1. Integration as an Inverse Process of Differentiation 2. Methods of Integration 3. Integrals of Some Particular Functions 4. Integration by Partial Fractions 5....
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JEE-Main - Grade 12 - Mathematics - Integrals - Target Setup for Integrals - Study ref# 919
Student requires to achieve the following milestones to get better grip over Integrals. The milestones / targets are as follows: Starting Point: Days 0Test TypeAppear on TestTarget TestsScorePractice Test000%Chapter Test000%Subje...
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JEE-Main - Grade 12 - Mathematics - Inverse Trigonometric Functions - Introduction and Snapshot of Inverse Trigonometric Functions - Study ref# 902
Introduction In this chapter, we shall study about the restrictions on domains and ranges of trigonometric functions which ensure the existence of their inverse and observe their behavior through graphical representations. Besides, some e...
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JEE-Main - Grade 12 - Mathematics - Application of Integrals - Introduction and Snapshot of Application of Integrals - Study ref# 920
Introduction In geometry, we have learnt formulae to calculate areas of various geometrical figures including triangles, rectangles, trapezias and circles. Such formulae are fundamental in the applications of mathematics to many real life...
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JEE-Main - Grade 12 - Mathematics - Application of Integrals - Introduction and Snapshot of Application of Integrals - Study ref# 921
Following sections must be covered to understand the Application of Integrals: 1. Area under Simple Curves 2. Area between Two Curves...
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JEE-Main - Grade 12 - Mathematics - Application of Integrals - Target Setup for Application of Integrals - Study ref# 922
Student requires to achieve the following milestones to get better grip over Application of Integrals. The milestones / targets are as follows: Starting Point: Days 0Test TypeAppear on TestTarget TestsScorePractice Test000%Chapte...
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JEE-Main - Grade 12 - Mathematics - Integrals - Study ref# 9490
Find an anti-derivative of the following function by the method of inspection.
Answer: Let
...
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JEE-Main - Grade 12 - Mathematics - Integrals - Study ref# 9491
Find an anti-derivative of the following function by the method of inspection.
Answer: Let I =
...
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JEE-Main - Grade 12 - Mathematics - Integrals - Study ref# 9492
Find an anti-derivative of the following function by the method of inspection.
Answer: Let
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JEE-Main - Grade 12 - Mathematics - Integrals - Study ref# 9493
Find the following integral:
Answer: Let I =
= ....
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JEE-Main - Grade 12 - Mathematics - Integrals - Study ref# 9494
Find the following integrals:
Answer: Let
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JEE-Main - Grade 12 - Mathematics - Integrals - Study ref# 9495
Find the following integrals:
Answer: Let I =
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JEE-Main - Grade 12 - Mathematics - Integrals - Study ref# 9496
Find the following integrals:
Answer: Let
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JEE-Main - Grade 12 - Mathematics - Integrals - Study ref# 9497
Find the following integrals:
Answer: Let
...
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JEE-Main - Grade 12 - Mathematics - Integrals - Study ref# 9498
Find the following integrals:
Answer: Let
...
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JEE-Main - Grade 12 - Mathematics - Integrals - Study ref# 9499
Integrate the function :
Answer: Let
Put
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JEE-Main - Grade 12 - Mathematics - Integrals - Study ref# 9500
Integrate the function :
Answer: Let
Put
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JEE-Main - Grade 12 - Mathematics - Integrals - Study ref# 9501
Integrate the function :
Answer: Let
Put
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JEE-Main - Grade 12 - Mathematics - Integrals - Study ref# 9502
Integrate the function :
Answer: Let
Put
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JEE-Main - Grade 12 - Mathematics - Integrals - Study ref# 9503
Integrate the function :
Answer: Let
Put
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JEE-Main - Grade 12 - Mathematics - Integrals - Study ref# 9504
Integrate the function :
Answer: Let
Put
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JEE-Main - Grade 12 - Mathematics - Integrals - Study ref# 9505
Integrate the function :
Answer: Let
Put
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JEE-Main - Grade 12 - Mathematics - Integrals - Study ref# 9506
Find the integral of the function:
Answer: Let
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JEE-Main - Grade 12 - Mathematics - Integrals - Study ref# 9507
Find the integral of the function:
Answer: Let
=
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JEE-Main - Grade 12 - Mathematics - Integrals - Study ref# 9508
Find the integral of the function:
Answer: Let
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JEE-Main - Grade 12 - Mathematics - Integrals - Study ref# 9509
Find the integral of the function:
Answer: Let
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JEE-Main - Grade 12 - Mathematics - Integrals - Study ref# 9510
Integrate the function:
Answer: Let
Put
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JEE-Main - Grade 12 - Mathematics - Integrals - Study ref# 9511
Integrate the function:
Answer: Let
Put
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JEE-Main - Grade 12 - Mathematics - Integrals - Study ref# 9512
Integrate the function:
Answer: Let
=
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JEE-Main - Grade 12 - Mathematics - Integrals - Study ref# 9513
Integrate the function:
Answer: Let
Put
...
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JEE-Main - Grade 12 - Mathematics - Integrals - Study ref# 9514
Integrate the rational function:
Answer: Let
Let
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JEE-Main - Grade 12 - Mathematics - Integrals - Study ref# 9515
Integrate the rational function:
Answer: Since
is an improper fraction, therefore we convert it into a proper fracti...
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JEE-Main - Grade 12 - Mathematics - Integrals - Study ref# 9516
Integrate the rational function:
Answer: Let
Let
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JEE-Main - Grade 12 - Mathematics - Integrals - Study ref# 9517
Integrate the rational function:
Answer: Let
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JEE-Main - Grade 12 - Mathematics - Integrals - Study ref# 9518
Integrate the rational function:
[Hint: multiply numerator and denominator by
and put ] Answer: Let
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JEE-Main - Grade 12 - Mathematics - Integrals - Study ref# 9519
Integrate the rational function:
Answer: Let
Let
, then
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JEE-Main - Grade 12 - Mathematics - Integrals - Study ref# 9520
Choose the correct answer:
equals (A)
(B)
(C)
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JEE-Main - Grade 12 - Mathematics - Integrals - Study ref# 9521
Integrate the function:
Answer: Let
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JEE-Main - Grade 12 - Mathematics - Integrals - Study ref# 9522
Choose the correct answer:
equals (A)
(B) (C)
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JEE-Main - Grade 12 - Mathematics - Integrals - Study ref# 9523
Evaluate the following definite integrals:
Answer: Let
then
...
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JEE-Main - Grade 12 - Mathematics - Integrals - Study ref# 9524
Evaluate the following definite integrals:
Answer: Let
then
Answer: Let
……….(i) Also,
and the circle . Hints- Firstly find the intersection point of and in the first quadrant and t...
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JEE-Main - Grade 12 - Mathematics - Application of Integrals - Study ref# 9538
The area between
and is divided into two equal parts by the line find the value of a. Answer: Given curve
is a parab...
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JEE-Main - Grade 12 - Mathematics - Application of Integrals - Study ref# 9539
Find the area bounded by the curve and the line . Hints – Find the points of intersection of line and . Find the proper limits, the required area is given by area under the parabola w.r.t. X-axis subtracted from ar...
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JEE-Main - Grade 12 - Mathematics - Application of Integrals - Study ref# 9540
Find the area of the circle which is interior to the parabola Hints- Draw a proper figure and find which area is required. Find the points of intersection and then integrate with proper limits. Answer: Given circle is
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JEE-Main - Grade 12 - Mathematics - Application of Integrals - Study ref# 9541
Find the area of the region bounded by the curves and Answer: Given curve
represents a parabola and it is symmetrical about Y-axis having vertex (0,2). The given region boun...
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JEE-Main - Grade 12 - Mathematics - Application of Integrals - Study ref# 9542
Using integration, find the area of the triangular region whose sides have the equations
and . Answer: Given equation of sides of the triangle are and On solving these equation...
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JEE-Main - Grade 12 - Mathematics - Application of Integrals - Study ref# 9543
Find the area enclosed between the parabola and the line. Answer: Given , the curve (represent a parabola with vertex (0,0)) &...
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JEE-Main - Grade 12 - Mathematics - Application of Integrals - Study ref# 9544
Using method of integration find the area bounded by the curve . Hints – Find the equations of all the lines enclosing the required area by using
in each quadrant and then, r...
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JEE-Main - Grade 12 - Mathematics - Application of Integrals - Study ref# 9545
Choose the correct answer: Area bounded by the curve , the X-axis and the coordinates and is (a) -9 (b)  ...
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JEE-Main - Grade 12 - Mathematics - Application of Integrals - Study ref# 9546
Choose the correct answer: The area of the circle exterior to the parabola is (a)
(b) (c) &nbs...
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JEE-Main - Grade 12 - Mathematics - Application of Integrals - Study ref# 9547
Using integration, find the area of the region bounded by the line ,X-axis and the lines and . Answer: Given equations of the curves are ………(i) ...
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