Let f be even and periodic with period T . If ∫ 0 a f ( x ) d x = 3 and ∫ − T /2 3 T /2 f ( x ) d x = 18 , find ∫ − a a + 5 T f ( x ) d x .

Question

Let f be even and periodic with period T . If ∫ 0 a ​ f ( x ) d x = 3 and ∫ − T /2 3 T /2 ​ f ( x ) d x = 18 , find ∫ − a a + 5 T ​ f ( x ) d x .

TestHub · Accepted Answer

The second integral covers two periods, so one-period integral is 9. Evenness gives ∫ − a a ​ f = 6 , while the next five periods contribute 45. Total: 51.

Mathematics - Definite Integration Question with Solution | TestHub

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