A spherical tank is half full of oil that has a density of 900 kg/m^3. Find the work required to pump the oil out of the spout on top. Use 9.8 for g and 3.14 for pi. Round to 3 sig. figs. The...

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Use cylindrical shells to compute the volume of a napkin ring of height 3h created by drilling a hole with radius r through the center of a sphere of radius R and express the answer in terms of h...

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Sketch the region in the xy-plane defined by the inequalities x − 3y2 ≥ 0, 2 − x − 5|y| ≥ 0 and find its area. If I did it correctly, I have a region defined by x=3y^2, (x-2)/5, -(x-2)/5...

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Y=8x^2 and x=8y^2 clearly (0,0) is one point of intersection. They should have another at I believe (1/8,1/8). How is that derived? TIA

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Integral from 0-t of e^-x/(1+(e^-x)) dx I let u = e^-x and du=-e^-x dx. Then it is -1 times the integral of 1/ (1+u) du from 1 to e^-t which equals -(ln(1+u) from 1to e^-t which...

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I need to integrate from 0-t. I am told to set u= Erf and u'= (2e^-x^2)/pi^1/2. v' is 1 and v=x. i am also told that the answer is t Erf(t)+ ((e^-t^2)-1)/pi^1/2 how many...

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Calculate an expression for the int from 1 to e of (ln(x))^k dx in terms of the integral from 1 to e of (ln(x))^k-1 dx. essentially, I need to integrate by parts to get this equality: The...