Question

Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. $$h(x) = \int_{4}^{x^2} \sqrt{2 + r^3} dr$$ $$h'(x) =$$

Name: use part 1 of the fundamental theorem of calculus to find the derivative of the function hx int4x2 sqrt2 r3 dr hx 67797
Uploaded: 2019-07-04T08:19:10-08:00
Duration: 45 s
Channel: Fuzail Shakir
Description: use part 1 of the fundamental theorem of calculus to find the derivative of the function hx int4x2 sqrt2 r3 dr hx 67797

          Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function.
$$h(x) = \int_{4}^{x^2} \sqrt{2 + r^3} dr$$
$$h'(x) =$$

Added by Douglas H.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Fuzail Shakir

07/04/2019

Step 1

If $F(x) = \int_{a}^{g(x)} f(t) dt$, then $F'(x) = f(g(x)) \cdot g'(x)$. In this problem, we have $h(x) = \int_{4}^{x^2} \sqrt{2 + r^3} dr$. Here, $f(r) = \sqrt{2 + r^3}$, $g(x) = x^2$, and $a = 4$. Show more…

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