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Set up an integral in spherical coordinates that represents the volume of the sphere x2+y2+z2=49x^2+y^2+z^2=49 in octant VII. Include bounds for your integral, but no need to evaluate.

Evaluate ∫1e ∫ln(y)1e(x2)y dxdy\int_1^{e}\ \int_{\ln(y)}^{1}{\frac{e^{(x^2)}}{y}\ dxdy} by switching the order of integration.

Using polar coordinates, evaluate ∫R∫ln(x2+y2) dA\int_R\int{\ln{(x^2+y^2)}\ dA} where RR is the washer 4≤x2+y2≤94\leq x^2+y^2 \leq 9 in quadrants I, II, and III.

Find the surface area of y2+z2+2x=0y^2+z^2+2x=0 with -2≤x≤0-2\leq x\leq 0.

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What is your favorite spring food?

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