Differentiate and integrate (1 Viewer)

Run hard@thehsc · Feb 15, 2022

I have done this before - but it was a long time ago: can someone please reexplain this to me:

For parts a and b if possible

5uckerberg · Feb 15, 2022

For this one, you see that $xe^{x}$ is two terms multiplied together right so thus you need to use the product rule to obtain $xe^{x}+e^{x}$ .

If you are integrating then you are going to notice a very important fact
$\frac{d}{dx}\left(xe^{x}\right)=xe^{x}+e^{x}$
$\int_{0}^{2}xe^{x}dx=\int_{0}^{2}\frac{d}{dx}\left(xe^{x}\right)-e^{x}dx$
Which then becomes
$\int_{0}^{2}xe^{x}dx=\int_{0}^{2}\frac{d}{dx}\left(xe^{x}\right)dx-\int_{0}^{2}e^{x}dx$
This is simply
$\left[xe^{x}-e^{x}\right]_{0}^{2}$
I reckon you can handle the rest and for part b use the same idea.

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Differentiate and integrate (1 Viewer)

Run hard@thehsc

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5uckerberg

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