Please show work

1. If we wish to evaluate the integral - f -dx by using a U-substitution, which choice for U would be appropriate? a. Inx b. - C. x2 d. *2 2. If we evaluate the integral J e*cosx dx by Parts, we will obtain which function? a. 2ex sinx b. cosx - sinx c. =ex(sinx + cosx) d. None of these 3. What integration technique would be appropriate to evaluate the integral S- 3x+ 1 x2-x-12 ax? a. U-Substitution b. Parts c. Partial Fractions d. Trig-Substitution 4. When finding the area between two curves, f (x) and g (x), over some interval, [a, b], if the curves cross each other twice then it would be necessary to split the integral into three integrals. These x-values are solutions to a. 3x = f(x) - g(x) b. f (x ) = g(x) C. X = n d. None of these 5. Which of the following would require us to split the integral to find the area enclosed by the two curves? a. Area enclosed by y = sinx, y = cosx over |0, " b. Area enclosed by y = x, y = x3 over [-1,1] c. Area enclosed by y = 4, y = x over [-4,4] d. None of these 6. Consider the volume of revolution problem below. Find the volume resulting from revolving the region enclosed by y = -x + 5 and y = = about the x-axis. What expressions describe the outer radius and the inner radius? a. Outer Radius = -x + 5, Inner Radius = > b. Outer Radius = =, Inner Radius = -x + 5 c. Outer Radius = = - x + 5, Inner Radius = 0 d. Outer Radius = -x + 5, Inner Radius = 2 - x - 57. A solid, S, is generated by parallel cross sections that are perpendicular to the xaxis. The base is an elliptical region with the boundary curve 9x2 + 43/2 = 36. The cross sections are isosceles right triangles with the hypotenuse lying on the base. Which of the following integrals will give the volume? a.f_22 (9 Zx2) dx b. I: (92352) dx of: l9Ex2 dx d.2f03(4x2) dx 8. When a particle is located a distance ofx feet from the origin, a force off(x) = 2x3 + x pounds acts on it. How much work is done in moving it from x = 1 to x = 4? Work = footpounds 9. What is the average value of the function y = f(x) shown on the TI84 screen below, over the interval [2, 7]? Hint: No integration is required. Average Value = Tl-84 Plus CE _ NIJRHL FLlJT UTIJ REL RDIH HP n 10. What trigonometric identity should you use to rewrite f Sin'lx dx so that it is integrable? a. Halfangle formula b. Doubleangle formula c. Pythagorean Identity d. None of these 11. What is the value of fonsin(8x)sin(6x) dx? Use the product to sum formulas in the textbook. a.E b.0 c d.T 2 ' 2 12. Write two integrals that give the volume described below. One should employ the Washer Method and the other should employ the Shell Method. DO NOT EVALUATE THE INTEGRALS. The region enclosed by the curves y = \\/x + 4 and y = + 2 revolved about the xaxis. Washer Method: ____ Shell Method: _ _____ x dx. SHOW ALL WORK. Hint: Use TrigSub with x = isin. 13. Evaluate the integral IW 14. Evaluate the definite integral So V1 - cos(40) de. SHOW ALL WORK. Hint: Use the identity cos(2x) = 1 - 2sinx 15. Evaluate S x2ex dx. SHOW ALL WORK