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,

$\int ^1_0g(x)dx=\frac{1}{2}\times1\times4=2$

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

$\int ^6_2g(x)dx=-\frac{1}{2}(\pi\times r^2)=-\frac{1}{2}(\pi\times2^2)=-2\pi=-6.28$