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Using properties evaluate the following definite integrals, evaluate the following: int_0^4 |x-1| dx |
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Answer» SOLUTION :`int_0^a f(X) g(x) dx = int_0^a f(a-x) g(a-x)dx` =`int_0^a f(a-x) [4- g(x)]dx` =`int_0^a 4 f(a-x) dx - int_0^a f(a-x) g(x) dx` =`4 int_f(a-x)dx - int_0^a f(x) g(x) dx` `gt 2 int_0^a f(x) g(x) dx = 4 int_0^a f(a-x)dx` = `4 int_0^a f(x) dx` THUS, `int_0^a f(x) g (x) dx = 2 int_0^a f(x) dx` |
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