In this page area using integration worksheet we are going to see some practice problems in the topic integration.
(1) Find the area of the region bounded by the line x  y = 1 and (i) x  axis, x = 2 and x = 4 (ii) x  axis , x =  2 and x = 0 

(2) Find the area of the region by the lune x  2 y  12 = 0 and (i) y  axis , y = 2 and y = 5 (ii) y  axis , y = 1 and y = 3 

(3) Find the area of the region bounded by the line y = x  5 and the x  axis between the ordinates x = 3 and x = 7. 

(4) Find the area of the region bounded by the curve y = 3 x²  x and the x  axis between x = 1 and x = 1. 

(5) Find the area of the region bounded by x² = 36 y , y  axis , y = 2 and y = 4  
(6) Find the area included between the parabola y² = 4 a x and its latus rectum.  
(7) Find the area of the region bounded by the ellipse (x²/9) + (y²/5) = 1 between the two latus rectum.  
(8) Find the area of the region bounded by the parabola y² = 4 x and the line 2 x  y = 4.  
(9) Find the common area enclosed by the parabolas 4 y² = 9 x and 3 x² = 16 y.  
(10) Find the area of the circle whose radius is a 
Find the volume of the solid that results when the region enclosed by the given curves:
(11) y = 1 + x²,x = 1 , y = 0 is revolved about the xaxis.  
(12) 2ay² = x(xa)² is revolved about xaxis,a>0.  
(13) y = x³ ,x = 0, y = 1 is revolved about the yaxis.  
(14) (x²/a²) + (y²/b²) = 1 is revolved about major axis a > b > 0  
(15) Derive the formula for the volume of a right circular cone with radius "r" and height "h"  
(16) The area of the region by the curve x y = 1,xaxis x =1. Find the volume of the solid generated by revolving the area mentioned about xaxis. 
area using integration worksheet area using integration worksheet