Inequalitiy 5 is greater than or equal to c
2 answers:
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(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: