Evaluating more integrals

(a) The integral is equal to the area of the triangle; it has height 20 and base 10, so the area is 20*10/2 = 100.

(b) The integral is equal to the area of the semicircle with radius 10. It's also under the horizontal axis, so the area is negative. The semicircle has area , so the integral is -50π.

(c) First compute

which is the area of the triangle on the right. It has height and base 5, so its area is 25/2.

Then split up the desired integral as

and plug in the integral values you know:

we need the options

step-by-step explanation: