Set4 - Math 21B-B - Homework Set 4 Section 5.6: 3. a. Z π...

This preview shows pages 1–5. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Math 21B-B - Homework Set 4 Section 5.6: 3. a. Z π 4 tan x sec 2 xdx Let u = tan x, du = sec 2 xdx . Z π 4 tan x sec 2 xdx = Z tan π 4 tan 0 udu = Z 1 udu = 1 2 u 2 1 = 1 2 (1) 2- 1 2 (0) 2 = 1 2 b. Z- π 4 tan x sec 2 xdx Z- π 4 tan x sec 2 xdx = Z tan 0 tan- π 4 udu = Z- 1 udu = 1 2 u 2 du = 1 2 (0) 2- 1 2 (- 1) 2 =- 1 2 6. a. Z √ 7 t ( t 2 + 1 ) 1 / 3 dt Let u = t 2 + 1 , du = 2 tdt . 1 Z √ 7 t ( t 2 + 1 ) 1 / 3 dt = Z 8 1 1 2 u 1 / 3 dt = 3 8 u 4 / 3 8 1 = 3 8 · 8 4 / 3- 3 8 · 1 4 / 3 = 6- 3 8 = 45 8 b. Z- √ 7 t ( t 2 + 1 ) 1 / 3 dt Z- √ 7 t ( t 2 + 1 ) 1 / 3 dt = Z 8 1 2 u 1 / 3 du =- Z 8 1 2 u 1 / 3 du =- 45 8 by (a.) 10. a. Z 1 x 3 √ x 4 + 9 dx Let u = x 4 + 9 , du = 4 x 3 dx Z 1 x 3 √ x 4 + 9 dx = Z 10 9 1 4 √ u du = Z 10 9 1 4 u- 1 / 2 du = 1 4 · 2 u 1 / 2 10 9 = 1 2 √ 10- 1 2 √ 9 = 1 2 √ 10- 3 2 b. Z- 1 x 3 √ x 4 + 9 dx 2 Z- 1 x 3 √ x 4 + 9 dx = Z 9 10 1 4 √ u du =- Z 10 9 1 4 √ u du = 3 2- 1 2 √ 10 by (b.) 23. a. Z 3 √ π 2 √ θ cos 2 θ 3 / 2 dθ Let u = θ 3 / 2 , du = 3 2 θ 1 / 2 = 3 2 √ θ dθ Z 3 √ π 2 √ θ cos 2 θ 3 / 2 dθ = Z π 2 3 cos 2 udu = Z π 2 3 1 2 + 1 2 cos(2 u ) du = Z π 1 3 + 1 3 cos(2 u ) du = u 3 + 1 3 · 1 2 sin(2 u ) π = h π 3 + 0 i- [0 + 0] = π 3 b. Z- 1 / 2- 1 t- 2 sin 2 1 + 1 t dt 3 Let u = 1 + 1 t , du =- 1 t 2 dt Z- 1 / 2- 1 t- 2 sin 2 1 + 1 t dt = Z- 1- sin 2 udu = Z- 1 sin 2 udu = Z- 1 1 2- 1 2 cos(2 u ) du = u 2- 1 2 · 1 2 sin(2 u )- 1 = (0- 0)-- 1 2- 1 4 sin(- 2) = 1 2- 1 4 sin(2) 30....
View Full Document

This note was uploaded on 11/17/2010 for the course MAT 21B MAT 21B taught by Professor Mat21b during the Spring '07 term at UC Davis.

Page1 / 11

Set4 - Math 21B-B - Homework Set 4 Section 5.6: 3. a. Z π...

This preview shows document pages 1 - 5. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online