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Test: Area Between Two Curves - JEE MCQ


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10 Questions MCQ Test - Test: Area Between Two Curves

Test: Area Between Two Curves for JEE 2024 is part of JEE preparation. The Test: Area Between Two Curves questions and answers have been prepared according to the JEE exam syllabus.The Test: Area Between Two Curves MCQs are made for JEE 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Area Between Two Curves below.
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Test: Area Between Two Curves - Question 1
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The area between the curves y = x2 and y = x3 is:​

Detailed Solution for Test: Area Between Two Curves - Question 1

y = x2 and y = x3 
To find point of intersections :
x2 = x3
x2(x-1) = 0
So, x = 0,1
POI are (0,0) & (1,1)

= [x3/3 – x4/4]x=1   - [x3/3 – x4/4]x=0
= (1/3 – 1/4) – (0)
= 1/12 sq units

Test: Area Between Two Curves - Question 2
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The area bounded by the curve y2 = 16x , x = 1, x = 3 and X-axis is: 

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Test: Area Between Two Curves - Question 3
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The shaded area is equal to:

​

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Test: Area Between Two Curves - Question 4
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The curves x2 + y2=16 and y2 = 6x intersects at​
Detailed Solution for Test: Area Between Two Curves - Question 4

x2 + y2=16 and y2 = 6x 
So, to figure out the P.O.I
x2 + 6x = 16
x2 + 6x – 16 = 0
(x+8) (x-2) = 0
x = -8, 2
For x = -8
y = (6*(-8))1/2 
= (-48)1/2 
No real value for y
For x = 2
y = (6*2)1/2 
= (12)1/2 
= 2*(3)1/2 
So, P.O.I is (2 , 2*(3)1/2 )    

Test: Area Between Two Curves - Question 5
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Find the area of region bounded by curve ​
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Test: Area Between Two Curves - Question 6
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The area of the region bounded by y = x2 – 2x and y = 4 – x2 is.​
Detailed Solution for Test: Area Between Two Curves - Question 6

To find area between y = x2 – 2x and y = 4 – x2,
We need to find POI.
x2 – 2x = 4 – x2
2x2 - 2x – 4 = 0
x2 – x – 2 = 0
(x-2)(x+1) = 0
x = -1, 2


= [(-2x3)/3 + x2 + 4x]x=2 - [(-2x3)/3 + x2 + 4x]x= -1
= -16/3 + 4 + 8 – (2/3 + 1 - 4)
= 9 sq units

Test: Area Between Two Curves - Question 7
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The shaded area enclosed between the parabolas with equations y = 1 + 10x – 2x2and y = 1 + 5x – x2 is equal to:
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Test: Area Between Two Curves - Question 8
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The area of the smaller region lying above the x-axis and included between the circle x2 + y2 = 2x and the parabola y2 = x.
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= π/4 – 2/3

Test: Area Between Two Curves - Question 9
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The area bounded by the curves f(x) = x2 + 1 and g(x) = x – 1 on the interval [1,3] is:​
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Test: Area Between Two Curves - Question 10
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The area shaded in the given figure can be calculated by which of the following definite integral?
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