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AP Calculus Quiz 4.1-4.5 Name_________________________ Evaluate the following integrals: 1. 6dx 2. (3x 2 2 x 5)dx 3. 4. 5 x 2 dx 3 sec 2 xdx 5. Find f (x) if f ( x) x 2 , f (0) 3 , and f (0) 1 . 6. a) What is a definite integral used to find? b) State one difference between an indefinite integral and a definite integral. 7. Use the properties of sigma notation and the summation formulas evaluate the given 10 sum: i 2 2i 3 7 f ( x)dx 8 and i 1 8. Given 0 7 1 f ( x)dx 3 , find 1 0 f ( x)dx . 9.State the Fundamental Theorem of Calculus using math symbols. 10. Use the Fundamental Theorem of Calculus to evaluate 2 1 1 dx . Show all work. x2 11. Evaluate: d x (2t 2 5) 2 dt 1 dx 12. Using a u-substitution, evaluate the following integral: x 8 4 x 2 dx Bonus: Use a(t ) 32 ft / s 2 as the acceleration due to gravity. A ball is thrown vertically upward from the ground with an initial velocity of 56 ft / s . For how many seconds will the ball be going upward?