If f is continuous and (0,4)∫ f(x) dx = -18, how to evaluate (0,2)∫ f(2x) dx ?

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If f is continuous and (0,4)∫ f(x) dx = -18, how to evaluate (0,2)∫ f(2x) dx ?

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Answer 1 · 2015-09-15T00:03:40

Refer to explanation

Explanation:

Assuming that you mean that

$\int_{0}^{4} f (x) d x = - 18$ $int_0^4 f(x)dx=-18$

and you want to evaluate $\int_{0}^{2} f (2 x) d x$ $int_0^2 f(2x)dx$

set $u = 2 x$ $u=2x$ hence $d u = 2 d x$ $du=2dx$ and

$\int_{0}^{2} f (x) d x = \int_{0}^{4} (\frac{1}{2}) \cdot f (u) d u = (\frac{1}{2}) \cdot \int_{0}^{4} f (u) d u = (\frac{1}{2}) \cdot (- 18) = - 9$ $int_0^2 f(x)dx=int_0^4 (1/2)*f(u)du=(1/2)*int_0^4f(u)du=(1/2)*(-18)=-9$

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If f is continuous and (0,4)∫ f(x) dx = -18, how to evaluate (0,2)∫ f(2x) dx ?

1 Answer

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