int_{a-c}^{b-c} f(x+c) , dx = | vedclass

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Question

(A) Let $I = \int_{a-c}^{b-c} f(x+c) \, dx$. Substitute $x + c = t$. Then $dx = dt$. When $x = a - c$,$t = (a - c) + c = a$. When $x = b - c$,$t = (b

Vedclass · Accepted Answer

$\int_{a}^{b} f(x) \, dx$

Vedclass · Answer

(A) Let $I = \int_{a-c}^{b-c} f(x+c) \, dx$. Substitute $x + c = t$. Then $dx = dt$. When $x = a - c$,$t = (a - c) + c = a$. When $x = b - c$,$t = (b - c) + c = b$. Substituting these into the integral,we get: $I = \int_{a}^{b} f(t) \, dt$. Since the variable of integration is a dummy variable,we can write $f(t) \, dt$ as $f(x) \, dx$. Therefore,$I = \int_{a}^{b} f(x) \, dx$.

$\int_{a-c}^{b-c} f(x+c) \, dx = $

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