DEFINITE INTEGRAL INVOLVING SQUARE ROOT

Problem 1 :

Solution :

Problem 2 :

Solution :

Problem 3 :

Solution :

Problem 4 :

Solution :

Problem 5 :

Find the area bounded by 

y = √x, the x-axis, x = 1 and x = 4

Solution :

Problem 6 :

Find the area bounded by 

y = x √x, the x-axis, x = 1 and x = 9

Solution :

y = x (x)^1/2

y = x^3/2

Applying some random values of x,

Some of the points on the curve are (1, 1) (4, 8) and (9, 27). By connecting these points, we will get

Problem 7 :

Solution :

The given shape is a rectangular hyperbola.

Solution :

Problem 8 :

Solution :

Problem 9 :

The shaded region has area 5 square units. Find k to the 3 decimal places.

Solution :