Solutions to Application Problems assigned in class (set 1)

Find the area between sin x and cos x (one "cell"):

Find the volume of a pyramid with an equilateral triangle base of side length 2 and height 6:

Find the volume of the solids of revolution:

between y = x^2 and y = x^4, about x = 7:

between y = x^3 and y = 4x, about about y = b (I said y = 20 in the morning class and changed it to something else, which I don't remember, in the afternoon class; this formula is valid for any b≥8.

between y = ln x, y = 0, x = 2, about x = -3:

Find work:

Roll up a 40 ft chain 1/4 of the way, with a 20 lb bucket on the end (chain weighs 2 lb/ft)

Pump all the water out of a cone (with sharp end down) with radius 2 ft, height 8 ft

Pump half the water out of a sphere of radius 5 ft

Find the fluid force ("hydrostatic force"):

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Created by Mathematica  (March 21, 2004)