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

2024
Views:

257

Pages:

3
Author:

Jalen W.

Instructor: Neelam Aggarwal Course: Spring 2022 - Calculus I (MATH1441-02F) Student: Jalen Wilson Date: 07/12/24 Assignment: Section 5.5 Enhanced Assignment 1. Evaluate the following indefinite integral by using the given substitution to reduce the integral to standard form. ∫ 3(3x + 12)5 dx, u = 3x + 12 ∫ 3(3x + 12)5 dx = 1 6 6 (3x + 12) + C 2. Evaluate the indefinite integral by using the substitution u = 9 − x5 to reduce the integral to standard form. 4 x ∫ 9−x dx 5 2 4 ∫ x 1 dx = 5 2 5 −1 9−x 5 9−x +C 3. Find the indefinite integral. ∫ x x−2 dx 3 ∫ x x−2 dx = 2 3 (x − 2) 2 1 + 4(x − 2) 2 +C 4. Evaluate the integral. ∫ p(p + 3)4 dp ∫ p(p + 3) dp = 4 (p + 3) 6 − 6 3(p + 3) 5 5 +C 5. Evaluate the integral. 2 x ∫ 6−x ∫ 3 2 dx 2 x 3 2 1 dx = 3 +C 3 6−x 6−x 6. Solve the initial value problem. ds dt 2 3 = 20t(5t − 3) , s(1) = 9 The solution is s = 1 2 2 5t − 3 4 +1 . 7. The velocity of a particle moving back and forth on a line is v = t= π 2 sec. The value of s when t = π sec is s = 2 (Type a simplified fraction.) 9 8. Evaluate the integral using the given substitution. ∫ x cos 2 5x x A. 2 dx, u = 5x 2 2 sin 5x 2 2 B. sin 5x 1 C. +C sin u + C u 1 D. +C 2 10 sin 5x +C 9. Evaluate the integral using the given substitution. ∫ 6(2x − 7)− 3 dx , A. − B. − 3 4 3 2 u = 2x − 7 (2x − 7) (2x − 7) C. − 3(2x − 7) D. (2x − 7) −2 −4 −2 −2 +C +C +C +C 10. Evaluate the integral using the given substitution. ∫ dx 6x + 2 A. 3 , u = 6x + 2 1 6x + 2 +C B. 2 6x + 2 + C 1 C. D. 6(6x + 2) 1 3 3/2 +C 6x + 2 + C m. ds dt = 9 sin (2t) m / sec for all t. If s = 0 when t = 0, find the value of s when 11. Evaluate the integral. x dx ∫ 5 2 7x + 3 A. − B. − C. − D. − 7 2 −4 2 −6 7x + 3 3 7 7x + 3 3 1 1 −6 2 −4 7x + 3 56 +C 2 7x + 3 14 +C +C +C 12. Evaluate the integral. ∫ x4 5 x + 9 dx A. B. C. 10 3 2 5 x +9 3 2 3/2 x +9 2 +C − 1/2 5 x +9 5 +C +C 3/2 5 15 D. − 3/2 5 x +9 13. Evaluate the integral. ∫ sin t dt (3 + cos t) 3 1 A. (3 + cos t) 2 2 B. (3 + cos t) 2 +C +C 1 C. 4(3 + cos t) 4 1 D. 2(3 + cos t) 2 +C +C +C