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If $ f $ is continuous and $ g $ and $ h $ are differentiable functions, find a formula for $$ \displaystyle \frac{d}{dx} \int^{h(x)}_{g(x)} f(t) \, dt $$

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03:17

Frank Lin

Calculus 1 / AB

Chapter 5

Integrals

Section 3

The Fundamental Theorem of Calculus

Integration

Campbell University

Baylor University

University of Nottingham

Lectures

05:53

In mathematics, an indefinite integral is an integral whose integrand is not known in terms of elementary functions. An indefinite integral is usually encountered when integrating functions that are not elementary functions themselves.

40:35

In mathematics, integration is one of the two main operations of calculus, with its inverse operation, differentiation, being the other. Given a function of a real variable (often called "the integrand"), an antiderivative is a function whose derivative is the given function. The area under a real-valued function of a real variable is the integral of the function, provided it is defined on a closed interval around a given point. It is a basic result of calculus that an antiderivative always exists, and is equal to the original function evaluated at the upper limit of integration.

03:12

If $f$ is continuous and $…

01:27

If $u$ and $v$ are differe…

01:28

Let $g$ and $h$ be differe…

01:34

03:13

Derive a formula for$$…

Derive a formula for $$\fr…

We know that if half of t is the anti derivative of lower case off of teeth and by the fundamental theme of calculus, we know half of h of acts menace off G of Axe gives us the integral from G F ax to H of X is off of DDT. Therefore, we know the derivative is gonna be just remember that you're multiplying by G prime of acts and H prime of X. Because remember these air, the chain and rules we have H and jeez, we must supply the chain rule.

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