I need it asap

3. HOMEWORK (1) Compute the integral (a) f sin(xx) dx by letting u = TX. (b) fex/2dx by letting u = x/2. Show that you got the correct answer by differentiating the computed function. (2) Compute the integral and then verify that you got the correct answer by differentiation. (a) fx2 4x3 + 7dx ( b) S: (3) Evaluate the definite integral (a) 2 V7 -2xdx (b) So te-12/2dt. (4) (a) Find the average value fnjab of fn(x) = sin(nx) on the interval [a, b]. (b) Based on a sample graph of fr (x) what do you expect about the tendency of the averages: fla,b], f2ja,b], . . .? Verify your expectation by formally computing lim fn[a,b]. n-+0o (5) The arc of the parabola y = x2 from (3,9) to (4, 16) is rotated about the y-axis. Find the area of the resulting surface. Please use Woframalpha only to check your final answer. Show all steps in solving the appropriate integral