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This contains 20 Multiple Choice Questions for GATE Test: Integral Calculus (mcq) to study with solutions a complete question bank.
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QUESTION: 1

Solution:

QUESTION: 2

Solution:

QUESTION: 3

Solution:

QUESTION: 4

Solution:

QUESTION: 5

Solution:

QUESTION: 6

Solution:

QUESTION: 7

Solution:

QUESTION: 8

Solution:

QUESTION: 9

Solution:

QUESTION: 10

Solution:

QUESTION: 11

If A is the region bounded by the parabolas y^{2} = 4x and x^{2} = 4y then is equal to

Solution:

QUESTION: 12

The area of the region bounded by the curves x^{2} + y^{2} = a^{2} and x + y = a in the first quadrant is given by

Solution:

The curves are

x^{2} + y^{2} = a^{2} ...(i)

and x + y = a ...(ii)

The curves (i) and (ii) intersect at A (a, 0) and B (0,a)

QUESTION: 13

The area bounded by the curves y = 2√x , y = -x , x = 1 and x = 4 is given by

Solution:

The given equations of the curves are

QUESTION: 14

The area bounded by the curves y^{2} = 9x , x - y + 2 = 0 is given by

Solution:

The equations of the given curves are

QUESTION: 15

The area of the cardioid r = a (1 + cos θ) is given by

Solution:

The equation of the cardioid is

r = a (1 + cos θ) .... (i)

If a figure is drawn then from fig. the required area is

QUESTION: 16

The area bounded by the curve r = θ cosθ and the lines θ = 0 and θ = π/2 is given by

Solution:

The equation of the given curve is

r = θ cosθ ...(i)

The required area

QUESTION: 17

The area of the lemniscate r^{2} = a^{2} cos2θ is given by

Solution:

If a figure is drawn then from fig. the required area is

QUESTION: 18

The area of the region bounded by the curve y(x^{2} + 2) = 3x and 4y = x^{2} is given by

Solution:

The equations of given curves are

y(x^{2} + 2) = 3x ....(i) and 4y = x^{2} ....(ii)

The curve (i) and (ii) intersect at A (2, 1).

If a figure is drawn then from fig. the required area is

QUESTION: 19

The volume of the cylinder x^{2} + y^{2} = a^{2} bounded below by z = 0 and bounded above by z = h is given by

Solution:

The equation of the cylinder is x^{2} + y^{2} = a^{2}

The equation of surface CDE is z = h

If a figure is drawn then from fig. the required area is

QUESTION: 20

Solution:

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