g(b) Use the Substitution Formula, f(g(x)) - g'(x) dx = f(u) du where g(x) = u, to evaluate the following integral. a g(a) 11 3( In x) 2 dx X . . . Determine a change of variables from y to u. Choose the correct answer below. O A. u= 3(Inx) OB. U=X O c. u= Inx OD. U= _ 3( In x) 2 X Write the integral in terms of u. 11 3( In x)2 X dx = ]du Evaluate the integral. 1 3 ( In x) 2 X -dx = (Type an exact answer.)Which of the following integrals, if either, calculates the area of the shaded region shown to the right? Give reasons for your answer. 1 1 a. I(x-(-x))dx= IZde -1 -1 Choose the correct answer below. i A. The integral in part b calculates the area of the shaded region because function y = - x is above the function y=x. B. The integral in part a calculates the area of the shaded region because function y = x is above the function y= x. i. C. Neither, because the graph of y = x is above the graph of y = - x for x 0. Find the total area of the shaded regions. The area is (Simplify your answer.) '09