MATH 205 Final: MATH 205 Louisville Practice Final 150417 Solution
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So now we wish to take the x2+1 ex + csc2 x + csc x cot x, and identifying these known forms. The rst term needs simpli cation, and the third term needs expansion; note that x2 1. Taking the antiderivative again to get f (x), we nd that f (x) = x3 9x + d,and since f (1) = 0, we require that. 1 9 + d = 0,or that d = 8. Thus, f (x) = x3 9x + 8. x2 ln(t2 7)dt. We do not know the antiderivative of ln(t2 7); let"s simply call it f (t). We"ll never need to know what it actually is, because the antiderivative and derivative will hopefully cancel out. 3x2f (x3) 2xf (x2) = 3x2 ln(x6 7) 2x ln(x4 7: (20 points) you have 1200 square centimeters of material with which to make a box with a square base and an open top.
