CBSE Class 12 Mathematics Application Of Integrals Worksheet Set A

Question. The area (in sq. units) of the region bounded by the parabola, y = x² + 2 and the lines, y = x + 1, x = 0 and x = 3, is :
(a) 15/4
(b) 21/2
(c) 17/4
(d) 15/2
Answer : D

Question. The area (in sq. units) of the region {x ∈ R : x ≥ 0, y ≥ 0, y ≥ x – 2 and y ≤ √x}, is
(a) 13/3
(b) 10/3
(c) 5/3
(d) 8/3
Answer : B

Question. The area (in sq. units) in the first quadrant bounded by the parabola, y = x² + 1, the tangent to it at the point (2, 5) and the coordinate axes is :
(a) 8/3
(b) 37/24
(c) 187/24
(d) 14/3
Answer : B

Question. The area of the region above the x-axis bounded by the curve y = tan x, 0 ≤ x ≤ π/2 and the tangent to the curve at x = π/4 is:
(a) 1/2 (log2 - 1/2)
(b) 1/2 (log2 + 1/2)
(c) 1/2 (1 - log2)
(d) 1/2 (1 + log2)
Answer : A

Question. The area (in sq. units) of the region {(x, y) : x ≥ 0, x + y ≤ 3, x² ≤ 4y and y ≤ 1 + √x } is :
(a) 5/2
(b) 59/12
(c) 3/2
(d) 7/3
Answer : A

Question. If the area enclosed between the curves y = kx² and x = ky², (k > 0), is 1 square unit. Then k is:
(a) √3/2
(b) 1/√3
(c) √3
(d) 2/√3
Answer : B

Question. The area (in sq. units) bounded by the parabola y = x² –1, the tangent at the point (2, 3) to it and the y-axis is:
(a) 8/3
(b) 32/3
(c) 56/3
(d) 14/3
Answer : A

Question. If the area of the region bounded by the curves, y = x², y = 1/x and the lines y = 0 and x = t (t > 1) is 1 sq. unit, then t is equal to 
(a) 4/3
(b) e^2/3
(c) 3/2
(d) e^3/2
Answer : B

Question. The area (in sq. units) of the smaller portion enclosed between the curves, x² + y² = 4 and y² = 3x, is :
(a) 1/√3 + π/3
(b) 1/2√3 + 2π/3
(c) 1/2√3 + 2π/3
(d) 1/√3 +4π/3
Answer : D

Question. The area bounded by the curve y = ln (x) and the lines y = 0, y = ln (c) and x = 0 is equal to :
(a) 3
(b) 3 ln (c) – 2
(c) 3 ln (c) + 2
(d) 2
Answer : D

Question. The parabolas y² = 4x and x² = 4y divide the square region bounded by the lines x = 4, y = 4 and the coordinate axes. If S₁ , S₂ , S₃ are respectively the areas of these parts/numbered from top to bottom; then S₁ : S₂ : S₃ is 
(a) 1 : 2 : 1
(b) 1 : 2 : 3
(c) 2 : 1 : 2
(d) 1 : 1 : 1
Answer : D

Question. The area (in sq. units) of the region {(x, y) : y² ≥ 2x and x² + y² ≤ 4x, x ≥ 0, y ≥ 0} is : 
(a) π - 4√2/3
(b) π/2 - 2√2/3
(c)π - 4/3
(d) π - 8/3
Answer : D

Question. The area (in sq. units) of the region described by A = {(x, y)| y ≥ x² – 5x + 4, x + y ≥ 1, y ≤ 0} is:
(a) 19/6
(b) 17/6
(c) 7/2
(d) 13/6
Answer : A

Question. The area (in sq. units) of the region described by {(x, y) : y² ≤ 2x and y ≥ 4x – 1} is 
(a) 15/64
(b) 9/32
(c) 7/32
(d) 5/64
Answer : B

Question. The area of the region bounded by the curves y = |x -1| and y = 3- |x| is 
(a) 6 sq. units
(b) 2 sq. units
(c) 3 sq. units
(d) 4 sq. units.
Answer : D

Question. The parabola y² = x divides the circle x² + y² = 2 into two parts whose areas are in the ratio 
(a) 9π + 2 : 3π – 2
(b) 9π – 2 : 3π + 2
(c) 7π – 2 : 2π – 3
(d) 7π + 2 : 3π + 2
Answer : B

Question. The area (in square units) of the region bounded by the curves y + 2x² = 0 and y + 3x² = 1, is equal to :
(a) 3/5
(b) 1/3
(c) 4/3
(d) 3/4
Answer : C

Question. Let A = {(x, y): y² ≤ 4x, y – 2x ≥ – 4}. The area (in square units) of the region A is:
(a) 8
(b) 9
(c) 10
(d) 11
Answer : B

Question. The area bounded by the parabola y² = 4x and the line 2x – 3y + 4 = 0, in square unit, is 
(a) 2/5
(b) 1/3
(c) 1
(d) 1/2
Answer : B

Question. The area under the curve y = | cos x – sin x |, 0 , ≤ X ≤ and above x-axis is :
(a) 2√2
(b) 2√2 - 2
(c) 2√2 + 2
(d) 0
Answer : B