Problem

Use a graph to give a rough estimate of the area …

01:19

Problem 74 Hard Difficulty

Verify that $ f(x) = \sin \sqrt[3]{x} $ is an odd function and use that fact to show that
$$ 0 \le \int^3_{-2} \sin \sqrt[3]{x} \, dx \le 1 $$

Answer

$\int_{a}^{b} f_{1}(x) d x \leq \int_{a}^{b} f(x) d x \leq \int_{a}^{b} f_{2}(x) d x$

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Video Transcript

we know that we can use the metric functions as a shortcut to figure out the integral. Which means we can see if we can prove if this function is odd or even. Okay. What this means is that where we have positive acts, we're now gonna plug in negative acts, and then we're gonna simplify. As you can see, we can see we end up with negative aftereffects, Which means that half of axe is indeed an odd function. Therefore, we know there's a property that from negative, eh? Awful vax D X is equivalent to zero. Therefore, we know that without even doing any mathematical calculations, we know the solution to this is going to be zero, and this is the proof that we can drive.

Amrita B.

Topics

Integrals

Integration

Calculus: Early Transcendentals

Chapter 5

Integrals

Section 5

The Substitution Rule

Problem

Use a graph to give a rough estimate of the area …

Problem 74 Hard Difficulty

Verify that $ f(x) = \sin \sqrt[3]{x} $ is an odd function and use that fact to show that
$$ 0 \le \int^3_{-2} \sin \sqrt[3]{x} \, dx \le 1 $$

Answer

$\int_{a}^{b} f_{1}(x) d x \leq \int_{a}^{b} f(x) d x \leq \int_{a}^{b} f_{2}(x) d x$

More Answers

Topics

Calculus: Early Transcendentals

Discussion

Top Calculus 1 / AB Educators

Heather Z.

Kayleah T.

Caleb E.

Joseph L.

Calculus 1 / AB Bootcamp

Precalculus Review - Intro

Functions on the Real Line - Overview

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Watch More Solved Questions in Chapter 5

Video Transcript

Topics

Calculus: Early Transcendentals

Top Calculus 1 / AB Educators

Heather Z.

Kayleah T.

Caleb E.

Joseph L.

Calculus 1 / AB Bootcamp

Precalculus Review - Intro

Functions on the Real Line - Overview

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Problem

Use a graph to give a rough estimate of the area …

Problem 74 Hard Difficulty

Verify that $ f(x) = \sin \sqrt[3]{x} $ is an odd function and use that fact to show that $$ 0 \le \int^3_{-2} \sin \sqrt[3]{x} \, dx \le 1 $$

Answer

$\int_{a}^{b} f_{1}(x) d x \leq \int_{a}^{b} f(x) d x \leq \int_{a}^{b} f_{2}(x) d x$

More Answers

Topics

Calculus: Early Transcendentals

Discussion

Top Calculus 1 / AB Educators

Heather Z.

Kayleah T.

Caleb E.

Joseph L.

Calculus 1 / AB Bootcamp

Precalculus Review - Intro

Functions on the Real Line - Overview

Recommended Videos

Watch More Solved Questions in Chapter 5

Video Transcript

Topics

Calculus: Early Transcendentals

Top Calculus 1 / AB Educators

Heather Z.

Kayleah T.

Caleb E.

Joseph L.

Calculus 1 / AB Bootcamp

Precalculus Review - Intro

Functions on the Real Line - Overview

Recommended Videos

Verify that $ f(x) = \sin \sqrt[3]{x} $ is an odd function and use that fact to show that
$$ 0 \le \int^3_{-2} \sin \sqrt[3]{x} \, dx \le 1 $$