Area Using Integration Worksheet





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



Solution

(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



Solution

(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.


Solution

(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.


Solution

(5) Find the area of the region bounded by x² = 36 y , y - axis , y = 2 and y = 4

Solution

(6) Find the area included between the parabola y² = 4 a x and its latus rectum.

Solution

(7) Find the area of the region bounded by the ellipse (x²/9) + (y²/5) = 1 between the two latus rectum.

Solution

(8) Find the area of the region bounded by the parabola y² = 4 x and the line 2 x - y = 4.

Solution

(9) Find the common area enclosed by the parabolas 4 y² = 9 x and 3 x² = 16 y.

Solution

(10) Find the area of the circle whose radius is a

Solution

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 x-axis.

(12) 2ay² = x(x-a)² is revolved about x-axis,a>0.

(13) y = x³ ,x = 0, y = 1 is revolved about the y-axis.

(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,x-axis x =1. Find the volume of the solid generated by revolving the area mentioned about x-axis.

area using integration worksheet  area using integration worksheet