Week4: Problem 1 Previous Problem Problem List Next Problem (1 point) Find the integral S q2 cos(3q) dq =Week4: Problem 2 (1 point) For each of the following integrals, indicate whether integration by substitution or integration by parts is more appropriate, or if neither method is appropriate. Do not evaluate the integrals. 1. f x sin x dx 0 A. substitution 0 B. integration by parts 0 C. neither x3 2. f H14 dx 0 A. neither 0 B. substitution 0 0. integration by parts 3. f x3e"4 dx 0 A. neither 0 B. substitution 0 C. integration by parts 4. f x3 cos(x4) dx 0 A. neither 0 B. substitution 0 0. integration by parts 5. f 2;? dx OA. integration by parts 0 B. substitution 0 C. neither Week4: Problem 3 Previous Problem Problem List Next Problem (1 point) Find the integral S x sin(x4) dx =Week4: Problem 4 (1 point) Estimate j; x3g' (x) dx where g(x) has the values given in the following table. To solve this exercise: 1. Use integration by parts to simplify the integral 2. Estimate the remaining integral using a Riemann sum (Note that one way to estimate the integral would be to assume that g(x) is a constant, or a linear function between the two endpoints; generate a more accurate estimate than that by using the provided table of data.) 3 / x3g'(x) dx = 0 Week4: Problem 5 (1 point) Using a calculator, find the area of the region under y = 3 111(6x) and above y = 7 for 2 S x S 4. area = Week4: Problem 6 Previous Problem Problem List Next Problem (1 point) Use a calculator or computer to find the value of the definite integral to four decimal places. So Cos 12 dx =Week4: Problem 7 (1 point) Use a computer algebra system to find an antiderivative F of such that F (0) = 0. F(x) = f(X) = xx +1 16 Week4: Problem 8 (1 point) Calculate the integral below, if it converges. If it does not converge, enter diverges for your answer. [10 1xe'"2 dx = Week4: Problem 9 (1 point) Calculate the integral, if it converges. If it diverges, enter diverges for your answer. Week4: Problem 10 Previous Problem Problem List Next Problem (1 point) Calculate the integral, if it converges. If it diverges, enter diverges for your answer. y dy V36-12 =