Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

i was reading special tutorial about evaluation line integral and author done following, he had to evaluate $$\int_{-1}^1 \cos(t)\,\sin^4(t)dt,$$ he did it by integration by part or denoted $u=\sin(t)$, $dv=\cos(t)dt$, got
$$\int_{-1}^1 u^4dv,$$ everything is clear still here but after integration he wrote it as
$$\frac{u^5}{5},$$ i know that $\int x^adx$ is equal $\frac{x^{a+1}}{a+1}$ but here $u^4 dv$ could not be just $\frac{u^5}{5}$, am i correct? i think it must be $$u^4v-v\int u^4 dt,$$ please tell me if i am wrong

share|improve this question
1  
I have edited your post so that the mathematics is in LaTeX, please feel free to edit the post if I have accidentally changed your intended meaning. –  Zev Chonoles Jul 22 '11 at 7:21

2 Answers 2

up vote 3 down vote accepted

It seems that what has happened here is just that $u$ and $v$ look awfully similar, and you have mistakenly thought the computation was an integration by parts (where we pick factors of the integrand, and label them $u$ (yoo) and $dv$ (dee vee)), when in fact it was a $u$-substitution (where we call some piece of the integrand $u$ (yoo), and express $du$ (dee yoo) in terms of our previous variable $t$ and its differential $dt$).


From user3196's explanation of the source below, here is a screenshot: enter image description here

Indeed, when setting up the substitution, the "$u$" part was distinctively serifed, while the "$du$" part was not. This inconsistency in the handwriting of the creator of this video is definitely the cause for the confusion.

share|improve this answer
    
♦ yes maybe i have made some mistake just here is link from youtube youtube.com/watch?v=fjEvsinvtnw –  dato datuashvili Jul 22 '11 at 7:36
    
♦ yes maybe i have made some mistake just here is link from youtube –  dato datuashvili Jul 22 '11 at 7:36

Looks to me like a typo. This is integration by substitution, not parts, and it should be $du=\cos t\,dt$.

share|improve this answer

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.