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

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

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

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

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

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

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

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

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

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

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

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

13.) The area of region is

(a) π/5                       (b) π/4

(c) π/4-1/2                 (d) π²/2

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

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

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

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

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

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

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