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Unformatted text preview: Practice problems for Final, MATH 10 B, 2010 Spring Chapter 5 : The definite integral 5 . 1 Using the table below, estimate R 6 g ( t ) dt using LEFT(3), RIGHT(3), and TRAP(3). t 2 4 6 g ( t ) 1 4 8 17 5 . 2 Write the integral representing the area between y = x 2- 2 and y = x and evaluate. 5 . 3 If in problem 5 . 2 , the x-axis is time and the y-axis is acceleration, what does the area you com- puted represent? 5 . 4 Let d dx F ( x ) = e- x 2 , and let F (- 2 ) = 0, F (- 1 ) = 0.135, F ( 1 ) = 1.63, F ( 2 ) = 1.76. Evaluate Z 1 2 e- x 2 dx . 5 . 5 The velocity of a car is v ( t ) = 70- t 3 . Is the car speeding up or slowing down? What is the average speed from time t = 2 to t = 4? Chapter 6 : Constructing Antiderivatives 6 . 1 Find the following antiderivatives. (a) Z dx (b) Z 5 dx (c) Z 1 x 3 dx (d) Z 1 x dx (e) Z e x dx (f) Z cos xdx (g) Z sin xdx (h) Z sec x tan xdx (i) Z sec 2 xdx (j) Z 1 1 + x 2 dx 6 . 2 Evaluate (a) d dx Z x 2 sin tdt (b) d dx Z 3 x 2 sin tdt 6 . 3 On Planet , the acceleration of gravity is- 20 ft/sec 2 . A rock is thrown vertically upward with a velocity of 20 ft/sec from the top of a 30 ft tower on Planet . (a) How long does it take the rock to reach its maximum height? (b) How long does it take the rock to hit the ground? (c) What is the speed at which the rock hits the ground? Chapter 7 : Integration 7 . 1 Find the following antiderivatives using one of the following 4 techniques : integration by sub- stitution, integration by parts, integration by trig substitution, or integration by partial fractions....
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This note was uploaded on 09/13/2010 for the course MATH math 10b taught by Professor Reed during the Summer '10 term at UCSD.
- Summer '10