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Show that int_0^a f(x) g(x) d x=2 int_0^a f(x) d x, if f and g are defined as f(x)=f(a-x) and g(x)+g(a-x)=4 |
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Answer» SOLUTION :`|X-1|` = {(x-1), x ge 1 `-(x-1), xlt 1`} therefore `int_0^4 |x-1| dx` =`int_0^1 (1-x) dx + int_1^4 (x-1) dx` =`(x-x^2/2)_0^1 + (x^2/2 -x)_1^4` `(1-1/2) +((16)/2 -4)-(1/2 -1)` `=1/2+4+1/2 = 5.` |
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