Question

Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. $$g(x)=\int_{3}^{x} e^{x^{2}-1} d t$$

Name: Problem 8, Chapter 5: Calculus
Uploaded: 2021-08-26T05:06:19-08:00
Duration: 1 min 25 s
Channel: Adrian Co
Description: Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. g(x)=∫3^x e^x^2-1 d t

   Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function.
$$g(x)=\int_{3}^{x} e^{x^{2}-1} d t$$

Calculus

James Stewart 4th Edition

Chapter 5, Problem 8

Instant Answer

Solved by Expert Adrian Co

08/26/2021

Step 1

e., $g(x) = \int_{a}^{x} f(t) dt$, then the derivative of $g(x)$ with respect to $x$ is just the function $f(x)$ itself. Show more…

Show all steps

Thanks for your feedback!

Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. $$g(x)=\int_{3}^{x} e^{x^{2}-1} d t$$

Play audio

Feedback

Adrian Co and 71 other subject Calculus 2 / BC educators are ready to help you.

Ask a new question

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Fundamental Theorem of Calculus Part 1

This theorem establishes the connection between differentiation and integration. It states that if a function is continuous on an interval, then the function defined by the integral of that function from a fixed lower limit to a variable upper limit is differentiable, and its derivative is the original integrand evaluated at the variable upper limit (provided the integrand is solely a function of the integration variable).

Differentiation Under the Integral Sign (Leibniz Rule)

This rule extends the Fundamental Theorem of Calculus to scenarios where the integrand depends on additional parameters or the variable of differentiation appears within the integrand. It provides a systematic way to differentiate an integral with respect to a parameter (or variable) by taking into account both the explicit dependence in the integrand and the effects due to varying limits of integration.

Please give Ace some feedback