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... read more

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.... read more

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... read more

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... read more

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... read more

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... read more

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... read more

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... read more

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... read more

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... read more

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 read more

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... read more

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... read more

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))
&... read more

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... read more

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) ... read more

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... read more

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)
... read more