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

Question 1.
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 2.
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 3.
The area of the region bounded by the curve y = $$\sqrt{16-x^2}$$ and x-axis is
(a) 8π sq.units
(b) 20π sq. units
(c) 16π sq. units
(d) 256π sq. units

Question 4.
Area of the region in the first quadrant enclosed by the x-axis, the line y = x and the circle x² + y² = 32 is
(a) 16π sq.units
(b) 4π sq. units
(c) 32π sq. units
(d) 24π sq. units

Question 5.
Area of the region bounded by the curve y = cos x between x = 0 and x = π is
(a) 2 sq. units
(b) 4 sq, units
(c) 3 sq.units
(d) 1 sq. units

Question 6.
The area of the region bounded by parabola y² = x and the straight line 2y = x is
(a) $$\frac{4}{3}$$ sq. unit
(b) 1 sq. unit
(c) $$\frac{2}{3}$$ sq. units
(d) $$\frac{1}{3}$$ sq. units

Answer: (a) $$\frac{4}{3}$$ sq. unit

Question 7.
The area of the region bounded by the curve y = sin x between the ordinates x = 0, x = $$\frac{π}{2}$$ and the x-axis is
(a) 2 sq. units
(b) 4 sq. units
(c) 3 sq. units
(d) 1 sq, unit

Question 8.
The area of the region bounded by the ellipse $$\frac{x²}{25}$$ + $$\frac{y²}{16}$$ = 1 is
(a) 20π sq. units
(b) 20π² sq. units
(c) 16π² sq. units
(d) 25π sq. units

Question 9.
The area of the region bounded by the circle x² + y² = 1 is
(a) 2π sq. units
(b) 7π sq. units
(c) 3π sq. units
(d) 4π sq. units

Question 10.
The area of the region bounded by the and the lines x = 2 and x = 3
(a) $$\frac{7}{2}$$ sq. unit
(b) $$\frac{9}{2}$$ sq. unit
(c) $$\frac{11}{2}$$ sq. units
(d) $$\frac{13}{2}$$ sq. units

Answer: (a) $$\frac{7}{2}$$ sq. unit

Question 11.
The area of the region bounded by the curve x = 2y + 3 and the lines y = 1 and y = -1 is
(a) 4 sq. units
(b) $$\frac{3}{2}$$ sq. units
(c) 6 sq. units
(d) 8 sq, units

Question 12.
If y = 2 sin x + sin 2x for 0 ≤ x ≤ 2π, then the area enclosed by the curve and x-axis is
(a) $$\frac{9}{2}$$ sq. units
(b) 8 sq. units
(c) 12 sq. units
(d) 4 sq. unjts

Question 13.
Tne area bounded by the curve y = x² – 1 and the straight line x + y = 3 is
(a) $$\frac{9}{2}$$ sq. units
(b) 4 sq. units
(c) $$\frac{7\sqrt{17}}{6}$$ sq. units
(d) $$\frac{17\sqrt{17}}{6}$$ sq. unjts

Answer: (d) $$\frac{17\sqrt{17}}{6}$$ sq. unjts

Question 14.
Area bounded by the lines y = |x| – 2 and y = 1 – |x – 1| is equal to
(a) 4 sq. units
(b) 6 sq. units
(c) 2 sq. units
(d) 8 sq. units

Question 15.
The area bounded by the lines y = |x| – 1 and y = -|x| + 1 is
(a) 1 sq. unit
(b) 2 sq. unit
(c) 2√2 sq. units
(d) 4 sq. units

Question 16.
The area of the region bounded by the line y = | x – 2 |, x = 1, x = 3 and x-axis is
(a) 4 sq. units
(b) 2 sq, units
(c) 3 sq. units
(d) 1 sq. unit

Question 17.
Area bounded by the ellipse $$\frac{x^2}{4}$$ + $$\frac{y^2}{9}$$ = 1 is
(a) 6π sq. units
(b) 3π sq. units
(c) 12π sq. units
(d) None of these

Question 18.
Area of triangle whose two vertices formed from the x-axis and line y = 3 – |x| is,
(a) 9 sq. units
(b) $$\frac{3}{2}$$ sq. units
(c) 3 sq. units
(d) None of these

Question 19.
The area of ellipse $$\frac{x^2}{4^2}$$ + $$\frac{y^2}{9^2}$$ = 1 is
(a) 6π sq. units
(b) $$\frac{π(a^2+b^2)}{4}$$ sq. units
(c) π(a + b) sq. units
(d) None of these

Question 20.
The area bounded by the lines |x| + |y| = 1 is
(a) 1 sq. unit
(b) 2 sq. units
(c) 2√2 sq. units
(d) 4 sq. units

Question 21.
The area bounded by the curve 2x² + y² = 2 is
(a) π sq. units
(b) √2π sq. units
(c) $$\frac{π}{2}$$ sq. units
(d) 2π sq. units

Question 22.
The area bounded by the curve x² = 4y + 4 and line 3x + 4y = 0 is
(a) $$\frac{25}{4}$$ sq. units
(b) $$\frac{125}{8}$$ sq. units
(c) $$\frac{125}{16}$$ sq. units
(d) $$\frac{124}{4}$$ sq. units

Answer: (d) $$\frac{124}{4}$$ sq. units

Question 23.
Area of the ellipse $$\frac{x^2}{a^2}$$ + $$\frac{y^2}{b^2}$$ = 1 is
(a) 4π ab sq. units
(b) 2π ab sq. units
(c) π ab sq. units.
(d) $$\frac{π ab}{2}$$ sq. units

Answer: (c) π ab sq. units.

Question 24.
Area bounded between the parabola y² = 4ax and its latus rectum is
(a) $$\frac{1}{3}$$ a sq. units
(b) $$\frac{1}{3}$$ a² sq. units
(c) $$\frac{8}{3}$$ a sq. units
(d) $$\frac{8}{3}$$ a² sq. units

Answer: (d) $$\frac{8}{3}$$ a² sq. units

Question 25.
The area bounded by the line y = 2x – 2, y = -x and x-axis is given by
(a) $$\frac{9}{2}$$ sq. units
(b) $$\frac{43}{6}$$ sq. units
(c) $$\frac{35}{6}$$ sq. units
(d) None pf these