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g(x)=int_(-12)^(x)(4t-7)dt

g^(')(5)=

$g(x)=\int_{-12}^{x}(4 t-7) d t$ $\newline$ $g^{\prime}(5)=$

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Evaluate definite integrals using the power rule

Full solution

Q.

g(x)=\int_{-12}^{x}(4 t-7) d t

\newline

g^{\prime}(5)=

Derivative Rule: We know that the derivative of an integral with respect to its upper limit is the integrand evaluated at that limit. $\newline$ So, $g'(x) = 4x - 7$ .
Evaluate at $x=5$ : Now we just plug in $x=5$ into $g'(x)$ to find $g'(5)$ . $\newline$ $g'(5) = 4(5) - 7$ .
Calculate $g'(5)$ : Calculate the value of $g'(5)$ . $g'(5) = 20 - 7$ .
Simplify Result: Simplify the result to get the final answer. $g'(5) = 13$ .

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