University:
Missouri State University
Course:
MTH 136 | Precalculus 1
Academic year:

2020
Views:

358

Pages:

5
Author:

Sadivt3v

Calculus - Worksheet 5.4 - KEY 1. int -2 ^ 3 (x+1) F-012 (x ^ 2 - 1) dx integrate x ^ 3 + x ^ 2 - x - 1 dx from - 2 to 3 1/4 * x ^ 4 + 1/3 * x ^ 3 - 1/2 * x ^ 2 -x| -2 ^ 3 L-L. 1 4 (3)^ 4 + 1 3 (3)^ 3 - 1 2 (3)^ 2 -3] - [1/4 * (- 2) ^ 4 + 1/3 * (- 2) ^ 3 - 1/2 * (- 2) ^ 2 - (- 2)] [81/4 + 21/3 - 9/2 - 3] - [16/4 - 8/3 - 4/2 + 2] [243/12 + 108/12 - 54/12 - 36/12] - [48/12 - 32/12 - 24/12 + 24/12] [261/12] - [16/12] 245/12 integrate (- 1/(sqrt(x)) + 2sqrt(x)) dx from 4 to 9 integrate - x ^ (- 1/2) + 2x ^ (1/2) dx from 4 to 9 -2x^ 1 2 + 4/3 * x ^ (3/2) | 4 ^ 9 [- 2sqrt(9) + 4/3 * (sqrt(9)) ^ 3] - [- 2sqrt(4) + 4/3 * (sqrt(4)) ^ 3] [- 2(3) + 4/3 * (3) ^ 3] - [- 2(2) + 4/3 * (2) ^ 3] [- 6 + 108/3] - [- 4 + 32/3] [- 6 + 36] - [- 12/3 + 32/3] [30]-[ 20 3 ] longrightarrow [40/3] - [20/3] = boxed 70 3 3. (-sinx)dx INTEGRATE cos* l_{0} ^ (2pi) L.L. [cos 2pi] - [cos 0] [1] - [1] int pi T (2sec^2 (2x)) dx 2 * 1/2 tan 2x|* 1 7 [tan 2 * pi/8] - [tan 2 * (- pi)/8] [tan(pi/4)] - [tan((- pi)/4)] [1] - [- 1] isin 이 @vad IV so fain is neg. 2 5. integrate 2/(x ^ 2) - x ^ (- 4/3) dx from 1 to 8 REWRITE 2x ^ - 2 + (- x ^ - 4) / 3 dx -2x^ -1 + 3x ^ (- 1/3) | 1 ^ 8 [- 2/8 + 3/(sqrt(8))] - [- 2/1 + 7/(8sqrt(1))] [- 1/4 + 3/2] - [- 2 + 3] [- 1/4 + 6/4] - [1] [5/4] - [4/4] a int pi/2 ^ pi/3 2cos 4x - 4sin 2xdx 2.7 sin U.L + 4 * 1/2 * cos 2 *| L ^ pi/2 [1/2 * sin 4 * pi/9 + 2cos 2 * pi/2] - [1/2 * sin 4 * pi/2 + 2cos 2 * pi/2] [1/2 * sin(pi/2) + 2cos(pi/4)] - [1/2 * sin - 2pi + 2cos - pi] [ 1 2 (1)+2( ( 2 2 )] - [1/2 * (0) + 2(- 1)] [1/2 + sqrt(2)] - [0 - 2] 1/2 + sqrt(2) + 2 5/2 + sqrt(2) integrate (2x)/((x ^ 2 + 2) ^ 2) dx from 0 to 1 integrate 2x * (x ^ 2 + 2) ^ - 2 dx from 1 to 1 u = x ^ 2 + 2 du = 2xdx 1.1. x = 0, u = 0 ^ 2 + 2 = 2 0.1. x = 1, u = 1 ^ 2 + 2 = 3 integrate u ^ - 2 du from 2 to 3 -1412 2. UL. L.L. [-]-[] - 2/6 + 3/6 8. integrate (3x ^ 2 - 2x + 3) ^ 3 * (3x - 1) dx from 0 to (2) u = 3x ^ 2 - 2x + 3 du = 6x - 2dx 1/2 * du = 3x - dx 1.1. X=0, u = 3 * (0) ^ 2 - 2(0) + 3 = 3 ul. x = 2 u = 3 * (2) ^ 2 - 2(2) + 3 = 11 1 * integrate u ^ 3 du from 3 to M えび 3 L.L. [1/8 * (11) ^ 4] - [1/8 * (3) ^ 4] [14641/8] - [81/8] 14560 8 1820