SC Calculus Integration And Functions Exercises

Calculus Integration Review 1. Find the position function s (t ) if a (t ) = −10 t , v (0) = 15 , and s (0) = 24 . 2. State the definition of a definite integral. 3. (a) State the fundamental theorem of calculus (both parts). (b) Assume part 2 is true and use it to prove part 1. 3 4. (a) Approximate ∫ 2x dx using a Riemann sum with n = 4 and right-hand endpoints. 1 (b) Find the exact area by taking the limit of the Riemann sum. Find the following integrals: ( ) 5. ∫ 2x 2 + x x dx 8. ∫ 1 10. ∫ r 2 (4r 3 + 1) dr 9. ∫ y 5 y 3 + 1 dy 0 11. x ∫ x cos (5 x ) dx 2 7. 6. ∫ sin θ cos θ dθ ∫ 2 −2 4 − x 2 dx Chapter 4 Review (p. 349) #2, 3, 11, 17, 19, 21, 25, 29, 46, 47 8 − x2 dx 3 −1 12. d x t cos (t − 1) dt dx ∫ 0 2 3

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