These are questions of Math 1B, which are calculus problems.

19. Evaluate: a f eSxl dx b [xi2d): c f x(x:+8) d f (1+:x)3 dx e. f x cos(5x) dx f fflgzydy g. Use substitution, followed by integration by parts: I cos J2? dx 20. Evaluate. 1 a- f 9.2de b. [02 V1 + 4x2dx Try trig substitution followed by table entry #38, or try using table entry #76. Check that both approaches give you the same result. 21. Describe in your own words: the integration method of partial fraction decomposition. Net change 22. A cyclist rides down a long straight road at velocity 170:) = 400 201: (meters per minute) for 0 S t S 10, where t is measured in minutes. How far (meters) has the cyclist traveled when her velocity is 340 meters/minute? 23. Suppose a particle moves along a straight line with velocity 170:), measured in feet per second, and acceleration a(t). a. What is the meaning of 51020 v(t)dt? b. What is the meaning of 1020 |v(t)|dt? . L = S V1+ (f'(x)) 2 dx . S = 2n Saf ( x ) 1+ (f' ( x ) ) 2 dx 24. (MC) Consider the shaded region, enclosed by the given curves: y = x + 2, , y = -x + 2, y = x2, x 2 0. Set up (but do not evaluate) an integral expression to find the area of the shaded region. A. S' Jy - (2 - y )dy + S Vy-(y- 2) dy B. J x2 - (2 - x) dx + f, x2 - (x + 2)dx C. S2 x2 - (x+ 2) - (-x+2) dx D. So Vy - (2 - y )dy + S, Vy - (y - 2) dy 25. Consider the graph ofy = e-2xon [0,2]. a. Set up, but do not evaluate, an integral that gives the length of the curve on the interval. b. Set up, but do not evaluate, an integral that gives the surface area of the shape obtained by rotating the curve about the x-axis.17. Sketch a graph that illustrates the statement that a continuous function on the interval [a, b] equals its average value at some point in (a, b) 18. Evaluate: a) Sx3 (2 + x4)5 dx b) S x2 vx3 + 1 dx c) S dt ( 1 - 6t ) 4 d) S cos3 0 sine do e) S sec2 (1/x) x2 dx f) S cos (" ) dt g) (4 evx VX dx h) re 4 dx x VIn x