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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 - Application of Integrals - Study ref# 9534
Find the area of the region bounded by the curve and the lines and the X-axis. Hints – The area enclosed by the curve , the X-axis and the ordinates is given by . Answer: The area of the region bounded...
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JEE-Main - Grade 12 - Mathematics - Application of Integrals - Study ref# 9535
Find the area of the region bounded by and the Y-axis in the first quadrant. Hints- To determine the required area, integrate x w.r.t. y and take as lower limit and as upper limit. Answer: The given curve
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JEE-Main - Grade 12 - Mathematics - Application of Integrals - Study ref# 9536
Find the area of the region bounded by the ellipse . Hints- Firstly, find the area in the first quadrant and then multiply by four (as in one quadrant there will be only ¼ part of the ellipse). Answer: The given cu...
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JEE-Main - Grade 12 - Mathematics - Application of Integrals - Study ref# 9537
Find the area of the region in the first quadrant enclosed by the X-axis and
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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