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Math 150A - Exam 3 Review

# Math 150A - Exam 3 Review - 2’ × 4’ a top measuring...

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Math 150A Midterm Exam 3 Review 1. Use the definition of the definite integral to evaluate the following: + + 2 0 2 ) 1 2 3 ( dx x x Use the right endpoints of the subintervals for your sample points. 2. What, exactly, does b a dt t f ) ( mean? 3. Evaluate the following definite integrals: a. ( 29 + - 4 0 2 ) cos( π dx x e x x b. - 2 ln 2 ln ) sinh( dt t 4. Use an appropriate substitution to evaluate each of the following integrals: a. dx x x 2 ) (ln b. - - 1 0 2 2 dy y e y e y y c. θ d ) tan( ) ( sec 4 d. + 3 ln 0 1 dt e e t t 5. Compute the area between the curves y = x 2 – 4 x + 5 and y = 2 x . 6. The area in problem 4 is revolved about the x -axis. What is the volume of the resulting solid? 7. The area in problem 4 is revolved about the y -axis. What is the volume of the resulting solid?

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8. What is the volume of a frustum of a rectangular cone with a base measuring
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Unformatted text preview: 2’ × 4’, a top measuring 1’ × 2’, and a height of 3’? 9. An object moves with velocity v ( t ) = t 3 + e t – 1. How far does the object move between the times t = 1 and t = 2? 10. Compute the average value of the following: a. f ( x ) = x 2 – 2 x + 3, 1 ≤ x ≤ 4 b. g ( t ) = cosh( t ), -ln(2) ≤ t ≤ ln(2) 11. The average value of x x f 1 ) ( = , 1 ≤ x ≤ t , is 0.1. What it t ? 12. A spring whose natural length is 2 feet requires a force of 100 pounds to keep it compressed to a length of 1.5 feet. How much work is required to compress the spring from a length of 1.5 feet to a length of 1 foot?...
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Math 150A - Exam 3 Review - 2’ × 4’ a top measuring...

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