4.5: #14 In problems 13 - 33, verify that F(x) is an antiderivative of the integrand f(x) and use Part 2 of the Fundamental Theorem to evaluate the definite integrals. 4 3 x 2 dx , F ( x )=x 3+ 2 14. 1 Section 4.6: #12, #22, #36 For problems 5 - 14 , use the suggested u to find du and rewrite the integral in terms of u and du. Then find an antiderivative in terms of u , and, finally, rewrite your answer in terms of x . 5+ x 3 7 dx x2 12. For problems 15 - 26 , use the change of variable technique to find an antiderivative in terms of x . 22. x 1x2 dx For problems 27 - 38 , evaluate the definite integrals. 5 1+2 x dx 36. 2 5 2 dx 2 1+ x 1 = 2 du u 2 2 ln|u| 2 ln|1+ x| 2 ln|1+ x|+ C 5 1+2 x dx=ln ( 36 )ln ( 9) 2 =ln(36)-ln(9) simplified = ln(4) Section 4.7: #10 In problems 7 - 18, sketch the graph of each function and find the area between the graphs of f and g for x in the given interval 10. f(x) = 4 - x 2 , g(x) = x + 2 and 0 x 2