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## Application of Integrals Class 12 MCQs Questions with Answers

Don’t forget to practice the multitude of MCQ Questions on Application of Integrals Class 12 with answers so you can apply your skills during the exam.

Question 1.

Area lying in the first quadrant and bounded by the circle x² + y² = 4 and the lines x = 0 and x = 2 is

(a) π

(b) \(\frac { π }{2}\)

(c) \(\frac { π }{3}\)

(d) \(\frac { π }{4}\)

## Answer

Answer: (a) π

Question 2.

Area of the region bounded by the curve y² = 4x, y-axis and the line y = 3 is

(a) 2

(b) \(\frac { 9 }{4}\)

(c) \(\frac { 9 }{3}\)

(d) \(\frac { 9 }{2}\)

## Answer

Answer: (a) 2

Question 3.

Smaller area enclosed by the circle x² + y² = 4 and the line x + y = 2 is

(a) 2 (π – 2)

(b) π – 2

(c) 2π – 1

(d) 2 (π + 2).

## Answer

Answer: (b) π – 2

Question 4.

Area lying between the curves y² = 4x and y = 2 is:

(a) \(\frac { 2 }{3}\)

(b) \(\frac { 1 }{3}\)

(c) \(\frac { 1 }{4}\)

(d) \(\frac { 3 }{4}\)

## Answer

Answer: (b) \(\frac { 1 }{3}\)

Question 5.

Area bounded by the curve y = x³, the x-axis and the ordinates x = -2 and x = 1 is

(a) -9

(b) –\(\frac { 15 }{4}\)

(c) \(\frac { 15 }{4}\)

(d) \(\frac { 17 }{4}\)

## Answer

Answer: (b) –\(\frac { 15 }{4}\)

Question 6.

The area bounded by the curve y = x|x|, x-axis and the ordinates x = -1 and x = 1 is given by

(a) 0

(b) –\(\frac { 1 }{3}\)

(c) \(\frac { 2 }{3}\)

(d) \(\frac { 4 }{3}\)

## Answer

Answer: (c) \(\frac { 2 }{3}\)

Question 7.

The area of the circle x² + y² = 16 exterior to the parabola y² = 6x is

(a) \(\frac { 4 }{3}\) (4π – √3)

(b) \(\frac { 1 }{3}\) (4π + √3)

(c) \(\frac { 2 }{3}\) (8π – √3)

(d) \(\frac { 4 }{3}\) (8π + √3)

## Answer

Answer: (c) \(\frac { 2 }{3}\) (8π – √3)

Question 8.

The area enclosed by the circle x² + y² = 2 is equal to

(a) 4π sq. units

(b) 2√2 π sq. units

(c) 4π² sq. units

(d) 2π sq. units.

## Answer

Answer: (d) 2π sq. units.

Question 9.

The area enclosed by the ellipse \(\frac { x^2 }{a^2}\) + \(\frac { y^2 }{b^2}\) = 1 is equal to

(a) π²ab

(b) πab

(c) πa²b

(d) πab².

## Answer

Answer: (b) πab

Question 10.

The area of the region bounded by the curve y = x² and the line y = 16 is

(a) \(\frac { 32 }{3}\)

(b) \(\frac { 256 }{3}\)

(c) \(\frac { 64 }{3}\)

(d) \(\frac { 128 }{3}\)

## Answer

Answer: (b) \(\frac { 256 }{3}\)

Question 11.

The area of the region bounded by the y-axis, y = cos x and y = sin x, 0 ≤ x ≤ \(\frac { π }{2}\) is

(a) √2 sq. units

(b) (√2 + 1) sq. units

(c) (√2 – 1) sq. units

(d) (2√2 – 1) sq. units.

## Answer

Answer: (c) (√2 – 1) sq. units

Question 12.

The area of the region bounded by the curve x² = 4y and the straight line x = 4y – 2 is

(a) \(\frac { 3 }{8}\) sq. units

(b) \(\frac { 5 }{8}\) sq. units

(c) \(\frac { 7 }{8}\) sq. units

(d) \(\frac { 9 }{8}\) sq. units.

## Answer

Answer: (d) \(\frac { 9 }{8}\) sq. units.

Question 13.

The area (in sq. units) of the region:

{(x, y) : y² ≥ 2x and x² + y2 ≤ 4x, x ≥ 0, y ≥ 0} is

(a) π – \(\frac { 8 }{3}\)

(b) π – \(\frac { 4√2 }{3}\)

(c) \(\frac { π }{2}\) – \(\frac { 2√2 }{3}\)

(d) π – \(\frac { 4 }{3}\)

## Answer

Answer: (a) π – \(\frac { 8 }{3}\)

Hint:

y² = 2x is a parabola,

and x² + y² = 4x

⇒ (x – 2)² + y² = 4.

It is a circle having centre (2, 0) and radius 2 units.

∴ Reqd. area = Shaded region

Fill in the Blanks

Question 1.

The area of the quadrant of the circle x² + y² = 4 is …………….

## Answer

Answer: π sq. units.

Question 2.

The area enclosed by the circle x² + y² = a² is ……………….

## Answer

Answer: 2 π a² sq. units.

Question 3.

The area of the parabola y² = 4ax bounded by the latus-rectum is ………………

## Answer

Answer: \(\frac { 8 }{3}\) a² sq. umts.

Question 4.

The area bounded by y = x², x = 0, x = 2 and x-axis is ……………….

## Answer

Answer: \(\frac { 8 }{3}\) sq. units.

Question 5.

The area under the curve y = 2√x between x = 0 and x = 1 is ……………..

## Answer

Answer: \(\frac { 4 }{3}\) sq. units.

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