True False. If f is continuous and lim x ® ¥ f(x) = 0 then ò 0¥ f(x) dx converges.
True False. If ò 0¥ f(x) dx diverges, then lim x ® ¥ f(x) is not zero.
True False. If f is even and ò 0¥ f(x) dx converges, then so does ò -¥¥ f(x) dx.
True False. The volume of a shell is 2pxf(x).
True False. If two water tanks have the same volume of water, then the work required to empty them is equal.
True False. To compute Surface Area, we integrate Ö (1 + (f'(x))2).
True False. The region under 1+cos(x), over [0, 2p], is revolved around the x-axis. Then the best way to find the volume is the shell method.
True False. The first step to integrate x3+2x+1 over x2-5x-6 is to divide.
True False. The first step in integrating tan-1(x) is a subtitution.
True False. The first step in integrating 1 over x2+4x+5 is completing the square.
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