Application of Integrals - Online Test

Q1. The area bounded by the curve y =x, the x – axis and the ordinates x = 1 and x = -1 is given by
Answer : Option B
Explaination / Solution:



Q2. The area bounded by the curve y = x (x – 1 ) ( x – 2 ) and the x – axis is equal to
Answer : Option D
Explaination / Solution:



Q3. The area bounded by the curve y = 2x -  and the line x + y = 0 is
Answer : Option D
Explaination / Solution:

The equation y =  i.e.represents a downward parabola with vertex at ( 1, 1 ) which meets x – axis where y = 0 .i .e . where x = 0 , 2. Also , the line y = - x meets this parabola where – x =  i.e. where x = 0 , 3.
Therefore , required area is :


Q4.

The area bounded by the curves and the x- axis in the first quadrant is


Answer : Option A
Explaination / Solution:

To find area the curves y =  and x = 2y + 3 and x – axis in the first quadrant., We have ;
,( y – 3 ) ( y + 1) = 0 . y = 3 , - 1 . In first quadrant , y = 3 and x = 9.
Therefore , required area is ;



Q5.

The area bounded by the curves and  is equal to


Answer : Option D
Explaination / Solution:

Eliminating y, we get:

Required area:



Q6. The area bounded by the parabolas y=  is equal to
Answer : Option A
Explaination / Solution:



Q7. The area bounded by the parabolas y = 
Answer : Option D
Explaination / Solution:



Q8.
Answer : Option A
Explaination / Solution:

The tangents are
since .
It passes through ( -2 , 0 ).

The tangents are :

Required area :

Q9.

The area bounded by the angle bisectors of the lines is


Answer : Option B
Explaination / Solution:

The angle bisectors of the line given by  are x = 0 , y = 1. Required area : =

Q10. The area bounded by the curves y = equal to
Answer : Option B
Explaination / Solution: