Multiple choice ( Application of Integral)
Choose and write the correct option in the following question:(application of integral multiple choice)
1.) The area enclosed by the circle x² + y² = 2 is equal to
(a) 4π sq.units (b) 2√2π sq.units
(c) 4π² sq.units (d) 2π sq. units
Answer (d)
2.) The area enclosed by the ellipse 
is equal to
(a) π²ab sq.units (b) πab sq.units
(c) πa²b sq.units (d) πab² sq.units
Answer (b)
3.) The area bounded by the curves, y = √x, 2y + 3 = x and x-axis in the Ist quadrant is
(a) 9 sq.units (b) 27/4 sq.units
(c) 36 sq.units (d) 18 sq.units
Answer (a)
4.) The area of region bounded by the curve x² = 4y and the straight line x = 4y – 2 is
(a) 3/8 sq.units (b) 5/8 sq.units
(c) 7/8 sq.units (d) 9/8 sq.units
Answer (d)
5.) The area of the region bounded by the curve y =√(16 – x²) and x-axis is
(a) 8π sq.units (b) 20 π sq.units
(c) 16 π sq.units (d) 256 π sq.units
Answer (a)
6.) 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) 16 π sq.units (b) 4π sq.units
(c) 32 π sq.units (d) 24 sq.units
Answer (b)
7.) Area of 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
Answer (a)
8.) 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) 3/2 sq.units
(c) 6 sq.units (d) 8 sq.units
Answer (c)
9.) The area of the region bounded by the curve y = x² and the line y = 16 is
(a) 37/3 sq.units (b) 256/3 sq.units
(c) 64/3 sq.units (d) 128/3 sq.units
Answer (b)
10.) The area of the region bounded by the curve y² = 9x, y = 3x is
(a) 1 sq.units (b) 1/2 sq.units
(c) 4 sq.units (d) 14 sq.units
Answer (b)
11.) The area of the curve y = sin x between 0 and π is
(a) 2 sq.units (b) 4 sq.units
(c) 12 sq.units (d) 14 sq.units
Answer (a)
12.) The area of the region bounded by the curve ay² = x³, the y-axis and the lines y = a and y = 2a is
(a) 3 sq.units (b) 
sq.units
(c) 
sq.units (b) 1 sq.units
Answer (b)
13.) The area of region 
is
(a) π/5 (b) π/4
(c) π/4-1/2 (d) π²/2
Answer (c)
14.) The area of the region bounded by the curves x = at² and y = 2at between the ordinate corresponding to t = 1 and t = 2 is
(a) 
sq.units (b) 
sq.units
(c) 5π sq.units (d) None of these
Answer (a)
15.) The area of minor segment of the circle 
cut off by the line x = π/2 is
(a) 
sq.units
(b) 
sq.units
(c) 
sq.units
(d) None of these
Answer (a)
16.) The area of the region bounded by the curve y = x³ and y = x + 6 and x = 0 is
(a) 7 sq.units (b) 6 sq.units
(c) 10 sq.units (d) 14 sq.units
Answer (c)
17.) The area bounded by the curve y = 2√x included between the lines x = 0 and x = 1 is
(a) 4 sq.units (b) 3 sq.units
(c) 4/3 sq.units (d) None of these
Answer (c)
18.) The area under the curve 
included between the lines x = 0 and x = a is
(a) πa²/4 sq.units (b) a²/2 sq.units
(c) πa² sq.units (d) 4π sq.units
Answer (a)
19.) The area of the region bounded by the triangle whose vertices are (-1, 1), (0, 5) and (3, 2) is
(a) 15/2 sq.units (b) 15 sq.units
(c) 4 sq.units (d) 10 sq.units
Answer (a)
20.) The area of the region bounded by the line y – 1 =x, the x-axis and the ordinates x = -2 and x = 3 is
(a) 4/3 sq.units (b) 7/2 sq.units
(c) 17/2 sq.units (d) 16/3 sq.units
Answer (c)
