I am having trouble setting up this integral. (Image is attached) How do I know if the disk method, or washer method is more desirable? How do I calculate the boundaries or limits of the integral? Why would I use dy instead of dx?
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1 Answer
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Revolving around the y axis means each infinitely narrow washer is dy thick. Hence use dy and convert your equation to $x = 7y^2$. The outer radius of your washer is $R = 7$ and the inner radius $r = 7y^2$. The limits of integration are from $y = 0$ (the x axis) to $y = 1$ (y value of $\sqrt{\frac{x}{7}}$ at $x = 7$).
$$\int_0^1 \pi\big((7)^2 - (7y^2)^2\big) dy$$
