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Detailed Solution for Test: JEE Main 35 Year PYQs- Definite Integrals & Applications of Integrals - Question 1

Detailed Solution for Test: JEE Main 35 Year PYQs- Definite Integrals & Applications of Integrals - Question 2

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Detailed Solution for Test: JEE Main 35 Year PYQs- Definite Integrals & Applications of Integrals - Question 3

Detailed Solution for Test: JEE Main 35 Year PYQs- Definite Integrals & Applications of Integrals - Question 4

Test: JEE Main 35 Year PYQs- Definite Integrals & Applications of Integrals - Question 5

If y = f(x) makes +ve intercept of 2 and 0 unit on x and y axes and encloses an area of 3/4 square unit with the axes then

Detailed Solution for Test: JEE Main 35 Year PYQs- Definite Integrals & Applications of Integrals - Question 5

Test: JEE Main 35 Year PYQs- Definite Integrals & Applications of Integrals - Question 6

The area bounded by the curves y = lnx, y = ln |x|,y=| ln x | and y = | ln |x| | is

Detailed Solution for Test: JEE Main 35 Year PYQs- Definite Integrals & Applications of Integrals - Question 6

Test: JEE Main 35 Year PYQs- Definite Integrals & Applications of Integrals - Question 7

The area of the region bounded by the curves y = |x - 1| and y = 3 - |x| is

Detailed Solution for Test: JEE Main 35 Year PYQs- Definite Integrals & Applications of Integrals - Question 7

Test: JEE Main 35 Year PYQs- Definite Integrals & Applications of Integrals - Question 8

is equal to

Detailed Solution for Test: JEE Main 35 Year PYQs- Definite Integrals & Applications of Integrals - Question 8

Test: JEE Main 35 Year PYQs- Definite Integrals & Applications of Integrals - Question 9

Let f(x) be a function satisfying f '(x) = f(x) with f(0) = 1 and g(x) be a function that satisfies f(x) + g(x) = x^{2} . Then the value of the integral

Detailed Solution for Test: JEE Main 35 Year PYQs- Definite Integrals & Applications of Integrals - Question 9

Test: JEE Main 35 Year PYQs- Definite Integrals & Applications of Integrals - Question 10

The value of the integral

Detailed Solution for Test: JEE Main 35 Year PYQs- Definite Integrals & Applications of Integrals - Question 10

Detailed Solution for Test: JEE Main 35 Year PYQs- Definite Integrals & Applications of Integrals - Question 11

Detailed Solution for Test: JEE Main 35 Year PYQs- Definite Integrals & Applications of Integrals - Question 12

Detailed Solution for Test: JEE Main 35 Year PYQs- Definite Integrals & Applications of Integrals - Question 13

Detailed Solution for Test: JEE Main 35 Year PYQs- Definite Integrals & Applications of Integrals - Question 14

Test: JEE Main 35 Year PYQs- Definite Integrals & Applications of Integrals - Question 15

and then the value of is

Detailed Solution for Test: JEE Main 35 Year PYQs- Definite Integrals & Applications of Integrals - Question 15

Test: JEE Main 35 Year PYQs- Definite Integrals & Applications of Integrals - Question 16

The area of the region boun ded by the curves y = | x - 2 |, x = 1,x = 3 and the x-axis is

Detailed Solution for Test: JEE Main 35 Year PYQs- Definite Integrals & Applications of Integrals - Question 16

Detailed Solution for Test: JEE Main 35 Year PYQs- Definite Integrals & Applications of Integrals - Question 17

Test: JEE Main 35 Year PYQs- Definite Integrals & Applications of Integrals - Question 18

The area enclosed between the curve y = log_{e} (x +e) and the coordinate axes is

Detailed Solution for Test: JEE Main 35 Year PYQs- Definite Integrals & Applications of Integrals - Question 18

Test: JEE Main 35 Year PYQs- Definite Integrals & Applications of Integrals - Question 19

The parabolas y^{2} = 4x and x^{2} = 4y divide the square region bounded by the lines x = 4, y = 4 and the coordinate axes. If S_{1} , S_{2} , S_{3} are respectively the areas of these parts numbered from top to bottom; then S_{1} : S_{2} : S_{3} is

Detailed Solution for Test: JEE Main 35 Year PYQs- Definite Integrals & Applications of Integrals - Question 19

Test: JEE Main 35 Year PYQs- Definite Integrals & Applications of Integrals - Question 20

Let f (x) be a non – negative continuous function such that the area bounded by the curve y = f (x), x - axis and the

ordinates

Detailed Solution for Test: JEE Main 35 Year PYQs- Definite Integrals & Applications of Integrals - Question 20

Detailed Solution for Test: JEE Main 35 Year PYQs- Definite Integrals & Applications of Integrals - Question 21

Detailed Solution for Test: JEE Main 35 Year PYQs- Definite Integrals & Applications of Integrals - Question 22

Detailed Solution for Test: JEE Main 35 Year PYQs- Definite Integrals & Applications of Integrals - Question 23

Test: JEE Main 35 Year PYQs- Definite Integrals & Applications of Integrals - Question 24

is equal to

Detailed Solution for Test: JEE Main 35 Year PYQs- Definite Integrals & Applications of Integrals - Question 24

Test: JEE Main 35 Year PYQs- Definite Integrals & Applications of Integrals - Question 25

The value of denotes the greatest integer not exceeding x is

Detailed Solution for Test: JEE Main 35 Year PYQs- Definite Integrals & Applications of Integrals - Question 25

Test: JEE Main 35 Year PYQs- Definite Integrals & Applications of Integrals - Question 26

Then F(e) equals

Detailed Solution for Test: JEE Main 35 Year PYQs- Definite Integrals & Applications of Integrals - Question 26

Test: JEE Main 35 Year PYQs- Definite Integrals & Applications of Integrals - Question 27

The solution for x of the equation

Detailed Solution for Test: JEE Main 35 Year PYQs- Definite Integrals & Applications of Integrals - Question 27

Test: JEE Main 35 Year PYQs- Definite Integrals & Applications of Integrals - Question 28

The area enclosed between the curves y^{2} = x and y = | x | is

Detailed Solution for Test: JEE Main 35 Year PYQs- Definite Integrals & Applications of Integrals - Question 28

Test: JEE Main 35 Year PYQs- Definite Integrals & Applications of Integrals - Question 29

Then which one of the following is true?

Detailed Solution for Test: JEE Main 35 Year PYQs- Definite Integrals & Applications of Integrals - Question 29

Test: JEE Main 35 Year PYQs- Definite Integrals & Applications of Integrals - Question 30

The area of the plane region bounded by the curves x + 2y^{2} = 0 and x + 3y^{2} = 1is equal to

Detailed Solution for Test: JEE Main 35 Year PYQs- Definite Integrals & Applications of Integrals - Question 30

Test: JEE Main 35 Year PYQs- Definite Integrals & Applications of Integrals - Question 31

The area of the region bounded by the parabola (y – 2)^{2} = x –1, the tangent of the parabola at the point (2, 3) and the x-axis is:

Detailed Solution for Test: JEE Main 35 Year PYQs- Definite Integrals & Applications of Integrals - Question 31

Test: JEE Main 35 Year PYQs- Definite Integrals & Applications of Integrals - Question 32

denotes the greatest integer function, is equal to :

Detailed Solution for Test: JEE Main 35 Year PYQs- Definite Integrals & Applications of Integrals - Question 32

Test: JEE Main 35 Year PYQs- Definite Integrals & Applications of Integrals - Question 33

The area bounded by the curves y = cos x and y = sin x between the ordinates x = 0 and

Detailed Solution for Test: JEE Main 35 Year PYQs- Definite Integrals & Applications of Integrals - Question 33

Test: JEE Main 35 Year PYQs- Definite Integrals & Applications of Integrals - Question 34

Let p(x) be a function defined on R such that p '(x) = p'(1 – x), for all x ∈ [0, 1], p (0) = 1 and p (1) = 41. Then

Detailed Solution for Test: JEE Main 35 Year PYQs- Definite Integrals & Applications of Integrals - Question 34

Test: JEE Main 35 Year PYQs- Definite Integrals & Applications of Integrals - Question 35

The value of

Detailed Solution for Test: JEE Main 35 Year PYQs- Definite Integrals & Applications of Integrals - Question 35

Test: JEE Main 35 Year PYQs- Definite Integrals & Applications of Integrals - Question 36

The area of the region enclosed by the curves y = x, x = e, y = 1/x and the positive x-axis is

Detailed Solution for Test: JEE Main 35 Year PYQs- Definite Integrals & Applications of Integrals - Question 36

Test: JEE Main 35 Year PYQs- Definite Integrals & Applications of Integrals - Question 37

The area between the parabolas and the straight line y = 2 is :

Detailed Solution for Test: JEE Main 35 Year PYQs- Definite Integrals & Applications of Integrals - Question 37

*Multiple options can be correct

Test: JEE Main 35 Year PYQs- Definite Integrals & Applications of Integrals - Question 38

then g (x + π) equals

Detailed Solution for Test: JEE Main 35 Year PYQs- Definite Integrals & Applications of Integrals - Question 38

Test: JEE Main 35 Year PYQs- Definite Integrals & Applications of Integrals - Question 39

**Statement-1 :** The value of the integral

Detailed Solution for Test: JEE Main 35 Year PYQs- Definite Integrals & Applications of Integrals - Question 39

Test: JEE Main 35 Year PYQs- Definite Integrals & Applications of Integrals - Question 40

The area (in square units) bounded by the curves and lying in the first quadrant is :

Detailed Solution for Test: JEE Main 35 Year PYQs- Definite Integrals & Applications of Integrals - Question 40

Test: JEE Main 35 Year PYQs- Definite Integrals & Applications of Integrals - Question 41

The integral

Detailed Solution for Test: JEE Main 35 Year PYQs- Definite Integrals & Applications of Integrals - Question 41

Test: JEE Main 35 Year PYQs- Definite Integrals & Applications of Integrals - Question 42

The area of the region described by

Detailed Solution for Test: JEE Main 35 Year PYQs- Definite Integrals & Applications of Integrals - Question 42

Test: JEE Main 35 Year PYQs- Definite Integrals & Applications of Integrals - Question 43

The area (in sq. units) of the region described by {(x, y) : y^{2} __<__ 2x and y __>__ 4x – 1} is

Detailed Solution for Test: JEE Main 35 Year PYQs- Definite Integrals & Applications of Integrals - Question 43

Test: JEE Main 35 Year PYQs- Definite Integrals & Applications of Integrals - Question 44

The integral

Detailed Solution for Test: JEE Main 35 Year PYQs- Definite Integrals & Applications of Integrals - Question 44

Test: JEE Main 35 Year PYQs- Definite Integrals & Applications of Integrals - Question 45

The area (in sq. units) of the region {(x, y) : y^{2} __>__ 2x and x^{2} + y^{2} __<__ 4x, x __>__ 0, y __>__ 0} is :

Detailed Solution for Test: JEE Main 35 Year PYQs- Definite Integrals & Applications of Integrals - Question 45

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