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(Solved): Suppose f is continuous. Prove the following properties of integrals, a. abf(x)dx=ba ...

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Suppose

f

is continuous. Prove the following properties of integrals, a.

\int_{a}^{b} f (x) d x = \int_{- b}^{- a} f (- x) d x

b.

\int_{a}^{b} f (x + c) d x = \int_{a - c}^{b - c} f (x) d x

. c.

\int_{a}^{b} x f (x^{2}) d x = \frac{1}{2} \int_{a^{2}}^{b^{2}} f (x) d x

.

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(a) prove that
let    is given
put    and if x=a then t=-a and x=b then t=-b

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