# 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)**