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g(x)=int_(-12)^(x)(4t-7)dt g^(')(5)=

g(x)=∫−12x(4t−7)dt g(x)=\int_{-12}^{x}(4 t-7) d t \newlineg′(5)= g^{\prime}(5)=

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Evaluate definite integrals using the power ruleright chevron icon

Full solution

Q. g(x)=∫−12x(4t−7)dt g(x)=\int_{-12}^{x}(4 t-7) d t \newlineg′(5)= g^{\prime}(5)=
  1. Derivative Rule: We know that the derivative of an integral with respect to its upper limit is the integrand evaluated at that limit.\newlineSo, g′(x)=4x−7g'(x) = 4x - 7.
  2. Evaluate at x=5x=5: Now we just plug in x=5x=5 into g′(x)g'(x) to find g′(5)g'(5).\newlineg′(5)=4(5)−7g'(5) = 4(5) - 7.
  3. Calculate g′(5)g'(5): Calculate the value of g′(5)g'(5).g′(5)=20−7g'(5) = 20 - 7.
  4. Simplify Result: Simplify the result to get the final answer. g′(5)=13g'(5) = 13.

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