The graph of g consists of two straight lines and a semicircle

we have to evaluate the integral from the given graph

we know that integration of the function f(x) is nothing but the area under the curve f(x).

a)

we have to evaluate,

In the graph of g(x) we can see that between x = 0 and x = 10 g(x) is nothing but the right angled triangle with base 10 and height 20

we know that the area of right angled triangle is given by,

A = 1/2 * base * height

hence we can say that the area of right angled triangle with base 10 and height 20 is given by

A = 1/2 * 10 * 20 = 100

Hence we can say that,

b)

we have to evaluate,

In the graph of g(x) we can see that between x = 10 and x = 30 g(x) is nothing but the semicircle with radius 10

we know that area of a semicircle with radius r is given by,

Hence we can say that area of a semicircle with radius 10 is given by,

But we can see that semicircle is below x axis hence we can say that,

c)

we have to evaluate,

we can say that,

we have,

Hence we can say that,

 ----------------------------------------------------1)

now we will evaluate,

In the graph of g(x) we can see that between x = 30 and x = 35 g(x) is nothing but the right angled triangle with base 5 and height 5

we know that the area of right angled triangle is given by,

A = 1/2 * base * height

hence we can say that the area of right angle triangle with base 5 and height 5 is given by,

A = 1/2 * 5 * 5 = 25/2

Hence we can say that,

Put this value in equation 1) we can say that,