Is:f(x) dx

13. J (fJ - csc fJ cot fJ) dfJ 14. J sec t (sec t + tan t) dtJsin 2x16. --dxsin x45. The area of the region that lies to the right of the y-axis andto the left of the parabola x = 2y - y2 (the shaded region inthe figure) is given by the integral j~(2y - y2) dy. (Turn yourhead clockwise and think of the region as lying below thecurve x = 2y - y2 from y = 0 to y = 2.) Find the area of theregion.ffi 17-18 Find the general indefinite integral. Illustrate by graphingseveral members of the family on the same screen.17. f (cosx + ~x)dx19. f0 2 (6x 2 - 4x + 5) dx21. C (5l - 6/ + 14)dy23. f2 (3u + Vdu20. r (I + 2x - 4x 3 ) dx24. I(2v + 5)(3v - I) dv~ The boundaries of the shaded region are the y-axis, the liney = I, and the curve y = ~. Find the area of this region bywriting x as a function of y and integrating with respect to y(as in Exercise 45).25. r .Ji (I + t) dt26. f: j2i dt27. [I (4 y3 + :3)dylm fal x($ + ~) dx31. f -Jr dx33. fo" (4 sin fJ - 3 cos fJ) dfJ1"/4 I + cos 2 fJ35. 2 dfJo cos fJ37.f 64 I + ~ ~ dx.1 'Ix~t (x - 2lxl)dx28.r y + 5/I dyy330.r(X+~YdXr 3x - 232. ---dxI;;34. r/3sec fJ tan fJ dfJ,,/436.1"/3 sin fJ + sin fJ tan 2 fJ dfJo sec 2 fJf 8 X - I1 ~X240. 301 dxf3r./242. Jo I sin x I dx47. If w'(t) is the rate of growth of a child in kilograms per year,what does j~O w'(t) dt represent?48. The current in a wire is defined as the derivative of thecharge: let) = Q'(t). (See Example 3 in Section 3.7.) Whatdoes j~let) dt represent?~ If oil leaks from a tank at a rate of r(t) liters per minute attime t, what does j~20r(t) dt represent?50. A honeybee population starts with 100 bees and increasesat a rate of n'(t) bees per week. What does 100 + j~5n'(t) dtrepresent?51. In Section 4.7 we defined the marginal revenue function R'(x)as the derivative of the revenue function R(x), where x is thenumber of units sold. What does .I;;:: R'(x) dx represent?52. If I(x) is the slope of a trail at a distance of x kilometersfrom the start of the trail, what does Jil/(x) dx represent?ffi 43. Use a graph to estimate the x-intercepts of the curvey = x + x 2 - x 4 • Then use this information to estimate thearea of the region that lies under the curve and above thex-axis.53. If x is measured in meters and I(x) is measured in newtons,what are the units for j~OOI(x) dx?54. If the units for x are meters and the units for a(x) are kilogramsper meter, what are the units for da/dx? What unitsdoes J~a(x) dx have?