How Do You Solve Calculus Homework Problem Six Using LaTeX?

Aug 27, 2023

KungPeng Zhou

Homework Statement: Use to start learning calculus

Relevant Equations: In short, the knowledge of calculus is fine, but it is as simple as possible, not a mathematics major, before starting to learn calculus

How to solve the sixth problem?

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Aug 27, 2023

PeroK

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You need to make an effort yourself. See the homework help guidelines:

https://www.physicsforums.com/threads/homework-help-guidelines-for-students-and-helpers.686781/

Aug 27, 2023

PeroK

Science Advisor

Homework Helper

Insights Author

Gold Member

2023 Award

You might like to learn Latex for posting mathematics:

https://www.physicsforums.com/help/latexhelp

3. How can I write integrals and derivatives in LaTeX?

In LaTeX, integrals and derivatives can be written using specific commands. For example:

\[\int_{a}^{b} f(x) \, dx\]\[\frac{d}{dx} f(x)\]\]These commands will render the integral and derivative symbols properly in your document.

4. How do I include a specific calculus problem, like Problem Six, in my LaTeX document?

To include a specific calculus problem, you can simply type out the problem statement and use LaTeX commands to format any mathematical expressions. For example:

\section*{Problem Six}Solve the integral:\[\int x^2 \sin(x) \, dx\]\end{document}

This will correctly display the problem statement and the integral to be solved.

5. How can I format the solution to Problem Six using LaTeX?

To format the solution, you can use the 'align' environment for step-by-step calculations:

\section*{Solution to Problem Six}We use integration by parts:\begin{align*}u &= x^2 & dv &= \sin(x) \, dx \\du &= 2x \, dx & v &= -\cos(x) \\\int x^2 \sin(x) \, dx &= -x^2 \cos(x) + \int 2x \cos(x) \, dx \\&= -x^2 \cos(x) + \left( 2x \sin(x) - \int 2 \sin(x) \, dx \right) \\&= -x^2 \cos(x) + 2x \sin(x) + 2 \cos(x) + C\end{align*}\end{document}

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