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

2024
Views:

115

Pages:

3
Author:

Jalen W.

Instructor: Neelam Aggarwal Course: Spring 2022 - Calculus I (MATH1441-02F) Student: Jalen Wilson Date: 07/12/24 Assignment: Section 5.3 Enhanced Assignment 1. Find the most general antiderivative or indefinite integral. ∫ 2 4 + tan θ dθ 2 2 (Hint: 1 + tan θ = sec θ) ∫ 2 4 + tan θ dθ = 3θ + tan θ + c 2. Solve the following initial value problem. dr dθ = πsin πθ, r(1) = 3 r = − cos (πθ) + 2 (Type an exactanswer, using π asneeded.) 3. Find the most general antiderivative. ∫ 9e 4x − 2e −x dx A. 9 4x e − 2e − x + C 4 B. 9 4x 1 − x e + e +C 4 2 C. 4 4x e + 2e − x + C 9 D. 9 4x e + 2e − x + C 4 1 4. Use theMax-Min Inequality to find upper and lower bounds for the value of ∫ 1 2 dx. 0 1+x 1 For the value of ∫ 1 2 dx, the upper bound is 1 1 and the lower bound is 2 0 1+x 1 5. Use the inequality sin x ≤ x, which holds for x ≥ 0, to find an upper bound for the value of ∫ sin x dx. 0 1 The upper bound for the value of ∫ sin x dx is 0 (Type an integer or a simplifiedfraction.) 1 2 . . −4 6. Suppose that ∫ −7 −4 g(t) dt = − 6. Find ∫ −7 g(x) −6 −7 dx and ∫ − g(t) dt. −4 A. 1; − 6 B. − 1; 6 C. 0; − 6 D. 1; 6 7. Suppose that f and g are continuous and that 11 11 11 7 7 7 11 11 11 7 7 7 ∫ f(x) dx = − 4 and ∫ g(x) dx = 8. Find ∫ [3f(x) + g(x)] dx. A. 20 B. 12 C. − 4 D. 11 8. Suppose that f and g are continuous and that ∫ f(x) dx = − 2 and ∫ g(x) dx = 7. Find ∫ [f(x) − 5g(x)] dx. A. − 45 B. − 37 C. 33 D. − 9 9. Graph the integrand and use areas to evaluate the integral. 5 ∫ x dx 1 A. 24 B. 3 C. 6 D. 12 10. Graph the integrand and use areas to evaluate the integral. 5 ∫ 9x dx 0 A. 25 2 B. 225 C. 45 D. 225 2 11. Graph the integrand and use areas to evaluate the integral. 6 ∫ (2x + 12) dx −6 A. 72 B. 24 C. 144 D. 288 12. Evaluate the integral. 4 ∫ 2 2x + x + 9 dx 0 A. 30 B. C. 484 3 260 3 D. 29