If f is a continuous function,then which of t | vedclass

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(D) Given that $f$ is a continuous function. Consider the integral $I = \int_{-3}^{5} f(x) dx$. Let $x = t - 1$,then $dx = dt$. When $x = -3$,$t = -2$

Vedclass · Accepted Answer

$\int_{-3}^{5} f(x) dx = \int_{-2}^{6} f(x - 1) dx$

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(D) Given that $f$ is a continuous function. Consider the integral $I = \int_{-3}^{5} f(x) dx$. Let $x = t - 1$,then $dx = dt$. When $x = -3$,$t = -2$. When $x = 5$,$t = 6$. Substituting these into the integral,we get: $I = \int_{-2}^{6} f(t - 1) dt$. Since the variable of integration is a dummy variable,we can replace $t$ with $x$: $I = \int_{-2}^{6} f(x - 1) dx$. Thus,option $(d)$ is correct.

If $f$ is a continuous function,then which of the following is true?

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