# How do you use substitution to integrate #2piy(8-y^2/3)dy#?

You can simply multiply it out. No complicated substitution required. Looks like the Shell Method?

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To integrate (2\pi y(8 - \frac{y^{\frac{2}{3}}}{3}) , dy) using substitution:

- Let ( u = 8 - \frac{y^{\frac{2}{3}}}{3} ).
- Find ( du ) by differentiating ( u ) with respect to ( y ).
- Substitute ( u ) and ( du ) into the integral.
- Integrate the expression with respect to ( u ).
- Finally, resubstitute the original variable ( y ) back into the expression.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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