MAC 2233 Worksheet 10

University:
Florida Atlantic University
Course:
MAC 2233 | Survey of Calculus I
Academic year:

2025
Views:

183

Pages:

2
Author:

customer-8344897

Name(PRINT): Merline Michelio MAC 2233 Worksheet 10 Compute the indefinite integral. Integral (9/x^5 + cube_root(x^2) - e^(2x) + 8/x) dx. Integral (9x^(-5) dx) + Integral (x^(2/3) dx) - Integral (e^(2x) dx) + Integral (8x^(-1) dx) = -9x^(-4) / 4 + x^(7/3) / (7/3) - e^(2x) / 2 + 8 ln(x) Answer: -9x^(-4) / 4 + 3x^(7/3) / 7 - e^(2x) / 2 + 8 ln(x) A particle is moving along a straight line with velocity v(t) = 2t^3 - 4t cm/sec. Its distance after 3 seconds is 8cm. Find s(t), the distance travelled by the particle at t seconds. Integral (2t^3 dt) - Integral (4t dt) Integral (2t^3) = 2t^(3+1) / (3+1) = 2t^4 / 4 = t^4 / 4 Integral (4t) = 4t^(1+1) / (1+1) = 4t^2 / 2 = 2t^2 s(t) = t^4 / 2 - 2t^2 Use substitution to compute the following indefinite integrals. (a) Integral from 7x^8 e^(x^9) dx u = x^9 du/dx = 9x^8 dx = du / (9x^8) Integral 7x^8 e^u (du / (9x^8)) = 7/9 Integral e^u du Answer: 7/9 e^(x^9) (b) Integral from 7 / (9 - 5x) dx u = 9 - 5x du/dx = -5 dx = -du / 5 Integral 7 / u (-du / 5) = -7/5 Integral du / u = -7/5 ln(u) = -7/5 ln(9 - 5x) Answer: -7/5 ln(9 - 5x) (c) Integral from 6x / sqrt(3 + x^2) dx u = 3 + x^2 du/dx = 2x dx = du / (2x) Integral 6x / sqrt(u) (du / (2x)) = 3 Integral du / sqrt(u) = 3 Integral u^(-1/2) du Integral u^(-1/2) = u^(-1/2 + 1) / (-1/2 + 1) = u^(1/2) / (1/2) Answer: 6 (3 + x^2)^(1/2)

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