These few questions have been bugging me for hours, help would be appreciated

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- Apr 13th 2012, 12:18 PMqwerty31Integration
These few questions have been bugging me for hours, help would be appreciated

- Apr 13th 2012, 12:35 PMSironRe: Integration
1. What's the lower bound? Use the goniometric substitution

2. Use integration by parts. - Apr 14th 2012, 03:00 AMqwerty31Re: Integration
- Apr 14th 2012, 05:39 AMSironRe: Integration
- Apr 14th 2012, 05:47 AMHallsofIvyRe: Integration
so, dividing both sides by , . Because of that the substitution changes to . Generally speaking, any time you have a square root of a quadratic, you should consider a trig substitution. (Some people prefer hyperbolic functions which satisfy similar identities.)

As for your new question, first complete the square: .

Now the substitution x= t+ 1/3 changes to integrand to