Application of Integrals - Online Test

Q1. The area common to the circle  and the parabola  = 6ax is
Answer : Option C
Explaination / Solution:



Q2. The area of the region bounded by the curves y =  and y = 3 -  is
Answer : Option C
Explaination / Solution:



Q3. The area bounded by the curves y =  - 1 and y = - + 1 is
Answer : Option A
Explaination / Solution:

The graph of modulus function is V-shaped graph. Therefore , from graph , the area is = √2 × √2 =2.

Q4. The area bounded by the parabola  = x and the straight line 2y = x is
Answer : Option C
Explaination / Solution:



Q5.

The area bounded by the ellipse  and the straight line x + 3y = 3 is


Answer : Option A
Explaination / Solution:



Q6.

The area between the hyperbola  , then x – axis and the ordinates at a and b with a > b is :


Answer : Option C
Explaination / Solution:

Required area :
 = =
Q7. The area of the smaller portion of the circle cut off by the line x = 1 is
Answer : Option A
Explaination / Solution:



Q8. The area of the smaller segment cut off from the circle  by x = 1 is
Answer : Option C
Explaination / Solution:



Q9.

The area enclosed by the curve and the y – axis is


Answer : Option B
Explaination / Solution:



Q10.

The area bounded by the curves  is given by


Answer : Option A
Explaination / Solution:

Both  and  are symmetric about y – axis and on solving them we get :


required area :
 =