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Engineering Mathematics Question on Definite and indefinite integrals

If g(x)g(x) is a continuous function such that∫abg(x) dx=β\int_{a}^{b} g(x) \, dx = \betathen the correct statement(s), amongst the following, is/are:

A

∫a+1b+1g(x−1) dx=β\int_{a+1}^{b+1} g(x-1) \, dx = \beta

B

∫1−a21−b22g(1−2x) dx=β\int_{\frac{1-a}{2}}^{\frac{1-b}{2}} 2g(1-2x) \, dx = \beta

C

∫0b−ag(x+a) dx=β\int_{0}^{b-a} g(x+a) \, dx = \beta

D

∫0a−bg(a−x) dx=β\int_{0}^{a-b} g(a-x) \, dx = \beta

Answer

∫a+1b+1g(x−1) dx=β\int_{a+1}^{b+1} g(x-1) \, dx = \beta

Explanation

Solution

The correct option is (A): ∫a+1b+1g(x−1) dx=β\int_{a+1}^{b+1} g(x-1) \, dx = \beta,(C):∫0b−ag(x+a) dx=β\int_{0}^{b-a} g(x+a) \, dx = \beta