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

2024
Views:

190

Pages:

4
Author:

Jalen W.

Instructor: Neelam Aggarwal Course: Spring 2022 - Calculus I (MATH1441-02F) Student: Jalen Wilson Date: 07/12/24 1. Use the SubstitutionFormula, b g(b) a g(a) ∫ f(g(x)) • g′(x) dx = ∫ Assignment: Section 5.6 Enhanced Assignment f(u) du where g(x) = u, to evaluate the following integral. π 3 (3t) ∫ 53−sin dt. cos (3t) 0 π 3 (3t) ∫ 53−sin dt = cos (3t) ln 0 3 (Type an exactanswer.) 2 2. Find the total area of the shaded region. (Type an exactanswer, using π asneeded.) y 6 y=4 4 2 y = 4 cos 2 x x 0 The total area of the shaded region is π/ 2 π 3π/ 2 2π 2π . 3. Find the area of the shaded region enclosed by the following functions. y 90 y= −x+9 Set up the integral that gives the area of the shaded region. Select the correct choicebelow, and fill in the answer boxes within your choice. A. y = 81 − x 72 2 54 ∫ dx ∫ dy −9 36 B. 18 x -12-10 -8 -6 -4 -2 -18 2 4 6 8 10 12 − 19 -36 + ∫ dy ∫ dy 0 + 17 C. ∫ dx −9 + ∫ dx ∫ dx −8 + 9 D. ∫ dy − 19 The total area is . (Type an integer or a simplifiedfraction.) 4. Find the area of the region enclosed by the curves y = x2 − 6 and y = 3. The area of the region enclosed by the curves is (Type a simplified fraction.) 36 . 5. Find the area of the region enclosed by the functions. 6 3 y = x and y = x 3 The area of the region enclosed by the two functions is . 28 (Type an integer or a simplifiedfraction.) 6. Find the area of the region enclosed by the curves y2 − 2x = 7 and x − y = 4. The area of the region enclosed by the curves is (Simplify youranswer.) 128 3 . 7. Find the area of the region enclosed by the curves y = 8sin x and y = sin (8x), 0 ≤ x ≤ π. The area of the region enclosed by the curves is (Simplify youranswer.) 16 . 8. Use the substitution formula to evaluate the integral. π ∫ (1 + cos 5t)2 sin 5t dt 0 A. B. C. D. 1 15 1 5 8 15 8 3 9. Find the area of the shaded region. 6 A. y 9 2 B. 3 4 C. y=x−1 2 x 1 2 3 2 y = x − 4x + 3 -2 4 5 D. 6 25 6 41 6 -4 -6 10. Find the area of the shaded region. 4 A. y B. 2 11 6 19 3 x -3 -2 -1 1 -2 2 3 D. 2 -8 9 2 2 y=x −4 -4 -6 C. y = 2x + x − 6 8 3 11. Find the area enclosed by the given curves. 2 y = 2x − x , y = 2x − 4 A. B. C. D. 37 3 32 3 34 3 31 3 12. Find the area enclosed by the given curves. 2 y = x, y = x A. B. C. D. 1 2 1 6 1 3 1 12