Problem

(a) Show that $ 1 \le \sqrt{1 + x^3} \le 1 + x^3 …

05:09

Problem 78 Hard Difficulty

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

Answer

$f(h(x)) \cdot h^{\prime}(x)-f(y(x)) \cdot g^{\prime}(x)$

More Answers

03:17

Frank L.

Topics

Integrals

Integration

Book Cover for Calculus: Early Tra…

Calculus: Early Transcendentals

Chapter 5

Integrals

Section 3

The Fundamental Theorem of Calculus

Discussion

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Watch More Solved Questions in Chapter 5

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Video Transcript

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.

Amrita B.

Topics

Integrals

Integration

Book Cover for Calculus: Early Tra…

Calculus: Early Transcendentals

Chapter 5

Integrals

Section 3

The Fundamental Theorem of Calculus

Top Calculus 1 / AB Educators

Grace H.

Numerade Educator

Catherine R.

Missouri State University

Kristen K.

University of Michigan - Ann Arbor

Michael J.

Idaho State University