# MCQ Questions for Class 12 Maths Chapter 8 Application of Integrals with Answers

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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) $$\frac { π }{4}$$

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) $$\frac { 9 }{2}$$

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: (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: (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: (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: (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: (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: (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.

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: (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: (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: (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: (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: π sq. units.

Question 2.
The area enclosed by the circle x² + y² = a² is ……………….

Answer: 2 π a² sq. units.

Question 3.
The area of the parabola y² = 4ax bounded by the latus-rectum is ………………

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

Question 4.
The area bounded by y = x², x = 0, x = 2 and x-axis is ……………….

Answer: $$\frac { 8 }{3}$$ sq. units.

Question 5.
The area under the curve y = 2√x between x = 0 and x = 1 is ……………..

Answer: $$\frac { 4 }{3}$$ sq. units.