NCERT Solutions - Exercise Miscellaneous : Application of Integral

Question 1: Find the area under the given curves and given lines:

(i) y = x², x = 1, x = 2 and x-axis
 (ii) y = x⁴, x = 1, x = 5 and x -axis

ANSWER : - (i) The required area is represented by the shaded area ADCBA as

1. The required area is represented by the shaded area ADCBA as

Question 2: Sketch the graph of and evaluate

ANSWER : -The given equation is

The corresponding values of x and y are given in the following table.

On plotting these points, we obtain the graph of  as follows.

It is known that,

Question 3: Find the area bounded by the curve y = sin x between x = 0 and x = 2π

ANSWER : -The graph of y = sin x can be drawn as

∴ Required area = Area OABO Area BCDB

Question 4: Area bounded by the curve y = x³, the x-axis and the ordinates x = -2 and x = 1 is

A. - 9  
B. 
C.  
D. 

ANSWER : -

Thus, the correct answer is B.

Question 5:The area bounded by the curve, x-axis and the ordinates x = -1 & x = 1 is given by [Hint: y = x² if x > 0 and y = -x² if x < 0]

A. 0      
B.  
 C.  
 D. 

ANSWER : -

Thus, the correct answer is C.