Question

If \( g(x) \) is a continuous function such that\[ \int_{a}^{b} g(x) \, dx = \beta \]then the correct statement(s), amongst the following, is/are:

• A. \[ \int_{a+1}^{b+1} g(x-1) \, dx = \beta \]
• B. \[ \int_{\frac{1-a}{2}}^{\frac{1-b}{2}} 2g(1-2x) \, dx = \beta \]
• C. \[ \int_{0}^{b-a} g(x+a) \, dx = \beta \]
• D. \[ \int_{0}^{a-b} g(a-x) \, dx = \beta \]

Answer 1

The Correct Option is A, C

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