Question

The graph of g consists of two straight lines and a semi circle. Evaluate each

Answer 1

Given:

a)

`\int ^1_0g(x)dx`

Consider the shape included in the region from 0 to 1 of g(x).

The area is,

`\int ^1_0g(x)dx=(1)/(2)*1*4=2`

b) From x = to x = 6 includes the semi-circle. Its area is calculated as,

`\int ^6_2g(x)dx=-(1)/(2)(\pi* r^2)=-(1)/(2)(\pi*2^2)=-2\pi=-6.28`