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g(x)=int_(0)^(x)(5t^(2)-t)dt

g^(')(2)=

$g(x)=\int_{0}^{x}\left(5 t^{2}-t\right) d t$ $\newline$ $g^{\prime}(2)=$

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Evaluate definite integrals using the power rule

Full solution

Q.

g(x)=\int_{0}^{x}\left(5 t^{2}-t\right) d t

\newline

g^{\prime}(2)=

Find Derivative of $g(x)$ : First, let's find the derivative of $g(x)$ using the Fundamental Theorem of Calculus. $\newline$ $g'(x) = \frac{d}{dx} \int_{0}^{x} (5t^2 - t) dt$ $\newline$ $g'(x) = 5x^2 - x$
Evaluate $g'(x)$ at $x=2$ : Now, let's evaluate $g'(x)$ at $x=2$ .
$g'(2) = 5(2)^2 - 2$
$g'(2) = 5(4) - 2$
$g'(2) = 20 - 2$
$g'(2) = 18$

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