University:
Georgia Southern University
Course:
MATH 1441 | Calculus I
Academic year:

2024
Views:

425

Pages:

8
Author:

Jalen W.

Instructor: Neelam Aggarwal Course: Spring 2022 - Calculus I (MATH1441-02F) Student: Jalen Wilson Date: 07/12/24 1. Find an antiderivative of the given function. 5 x −3 3 10 2 A. x −3 3 3 B. 5x 2 − 3x 3 10 2 C. x − 3x 3 3 D. 5x 2 −3 2. Find an antiderivative of the given function. − 45 10 x A. 9 x B. 5 x C. 9 5 x D. 6 10 9 − 5 x 3. Find an antiderivative of the given function. −4 x + 1 3 x 1 1 2 2 A. − + x 4 3 4x 1 1 2 2 B. − + x 3 3 3x 1 1 2 2 C. − + x 3 3 4x 1 1 2 2 D. − + x 4 3 3x Assignment: Review: Sections 4.8, 5.3-5.6 4. Find an antiderivative of the given function. 4 cos 5x A. − 20 sin 5x B. sin 5x C. 4 5 sin 5x D. 4 sin 5x 5. Find an antiderivative of the given function. cos πx + 4 sin A. 1 π x 4 sin πx − 16 cos x 4 B. − sin πx − 16 cos C. 1 π sin πx − cos x 4 x 4 D. − π sin πx + cos x 4 6. Find an antiderivative of the given function. 2 csc 2x 3 x A. 6 cot B. 4 csc 3 2x 3 C. − 6 cot D. 2 3 cot x 3 x 3 cot x 3 7. Find an antiderivative of the given function. e − 7 4 x 7 4 − 4x e 7 A. 7 7 − 4x e 4 B. − 7 4 − x C. − e 4 7 D. e − 7 4 x 8. Find the most general antiderivative. ∫ t 2 6t + dt 8 1 A. 12t + +C 8 3 B. 18t + 1 2 t +C 4 3 C. 2t + t + C t 3 D. 2t + 2 16 +C 9. Find the most general antiderivative. ∫ y 8 + 7 y dy 3 A. 1 12 y 1 B. 16 2 + 14 y + C y− 1 14 y +C 3 C. 1 12 y 2 − 14 y + C 3 D. 3 16 y 2 + 1 14 y +C 10. Find the most general antiderivative. ∫ ( − 9 cos t)dt A. − sin t 9 +C B. − 9 cos t + C C. − 9 sin t + C D. − 9 sin t +C 11. Find the most general antiderivative. ∫ sin θ( cot θ + csc θ)dθ A. sin θ + θ + C B. sin θ + C C. cos θ + C D. csc θ + cos θ + C 12. Graph the integrand and use areas to evaluate the integral. 6 ∫ (2x + 12) dx −6 A. 144 B. 288 C. 72 D. 24 13. Find the total area of the region between the curve and the x-axis. 2 y = 2x − x ; 0 ≤ x ≤ 2 A. B. C. D. 7 3 5 3 4 3 2 3 14. Find the total area of the region between the curve and the x-axis. y= 3 x 3 ; 1 ≤ x ≤ 3 4 A. 3 1 B. 3 1 C. 2 D. 3 15. Find the total area of the region between the curve and the x-axis. 2 y = − x + 9; 0 ≤ x ≤ 5 A. B. C. D. 10 9 5 9 10 3 98 3 16. Evaluate the integral using the given substitution. ∫ x cos 2 8x 2 dx, u = 8x 2 A. x 2 sin 8x 2 2 B. sin 8x +C 1 2 C. D. 16 1 u sin 8x sin u + C +C +C 17. Evaluate the integral using the given substitution. 3 ∫ 20s ds 4 4 u=6−s , 6−s 10s A. 4 +C 4 6−s B. − 10s 3 4 6−s +C 4 C. − 10 6 − s + C −5 D. 2 6−s +C 4 18. Evaluate the integral using the given substitution. ∫ csc 2 7θ cot 7θ dθ , u = cot 7θ A. − B. 1 6 C. − D. 1 14 2 cot 7θ + C 3 2 csc 7θ cot 7θ + C 1 14 1 2 tan 7θ + C 2 14 cot θ + C 19. Evaluate the integral. ∫ x dx 5 2 7x + 3 A. − B. − C. − D. − 1 56 1 14 7 3 7 3 2 −4 2 −6 7x + 3 7x + 3 2 −4 2 −6 7x + 3 7x + 3 +C +C +C +C 20. Evaluate the integral. ∫ x5 6 x + 6 dx A. 4 x6 + 6 B. C. 2 3/2 6 3/2 6 3/2 x +6 3 1 x +6 9 1 D. − +C +C − 1/2 6 x +6 3 +C +C 21. Evaluate the integral. ∫ sin t dt (8 + cos t) 6 1 A. 7(8 + cos t) 7 1 B. 5(8 + cos t) 1 C. (8 + cos t) 5 5 D. (8 + cos t) 5 5 +C +C +C +C 22. Use the substitution formula to evaluate the integral. 0 ∫ −1 2t 3+t A. − B. 2 3 7 288 7 288 C. − D. − 7 144 7 72 dt 23. Use the substitution formula to evaluate the integral. 1 ∫ 0 4r dr 4 + 2r 2 6 A. 2 −1 B. − 2 6 + 4 6 −2 C. D. 2 6 − 4 24. Use the substitution formula to evaluate the integral. π ∫ (1 + cos 5t)2 sin 5t dt 0 A. B. C. D. 8 15 8 3 1 15 1 5 25. Evaluate the integral. 6 ∫ 2 3x + x + 5 dx 0 A. 119 B. 264 C. 47 D. 518