1. Integrate. (a) Z x p x + 3dx (b) Z x sin (x) cos (2x)dx 2. Integrate. (a) Z dx p 9×2 + 18x + 13 (b) Z sec2 (x) q 4 9 tan2 (x)dx (c) Z p x2 1 x2 dx 3. Use the midpoint rule to estimate the integral Z3 1 p x2 1 e2x 1 dx with n = 4. Evaluate as far as you can without using a calculator. 4. Evaluate the following integrals (a) Z sin3 (x) cos6 (x)dx, (b) Z 1 0 dx 2×2 12x , (c) Z (t + sin (t))2 dt. 5. Evaluate the following integrals. If they do not converge, state why. Do not use a calculator at any point. (a) Z1 0 ln r p r dr, (b) Z1 0 csc (x)dx, (c) Z1 1 xe xdx. 6. Let f(x) = x3+3 sin (x)+2 cos (x). Find the equation of the tangent line to the graph of f 1(a) when a = 2. Be sure to check all the things that need to be checked.

 

 

 

 

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