U-Substitution

[lamaclass]

I did not know how you would apply U-Substitution for these problems:

1. IN [(x[sup:3cvwy9xm]2[/sup:3cvwy9xm]+3x+7/x[sup:3cvwy9xm]1/2[/sup:3cvwy9xm])dx]

2. IN [t[sup:3cvwy9xm]2[/sup:3cvwy9xm](t-2/t)dt]

3. IN [(9-y)y[sup:3cvwy9xm]1/2[/sup:3cvwy9xm]dy]

 

[daon]

It isn't needed for the first. I suppose you could set u=x^(1/2) to make division easier. Top would become u^4+3u^2+7.

The second, well, is it supposed to be (t-2)/t or t-2/t in parentheses? If the former, it is a similar problem as above. Otherwise combine it to have (t^2-2)/t then it is like the above. Just divide.

The third one, I don't see how substitution would help at all.

 

[lamaclass]

Oh ok! I just wasn't sure how else to go about solving these in a way that would involve substitution. :?

 

[galactus]

We may be able to use a sub on the third one. See how this works. Assuming you have to use a u-sub.

\(\displaystyle \int (9-v)\sqrt{v}dv\)

Let \(\displaystyle u=\sqrt{v}, \;\ u^{2}=v, \;\ 2udu=dv\)

Then, we get:

\(\displaystyle 2\int(9-u^{2})u^{2}du\)

\(\displaystyle \int(18u^{2}-2u^{4})du=18\int u^{2}du-2\int u^{4}du\)

 

[daon]

Personally, I wouldn't for any of these (either now or when I was a calculus student). Is the title of the text "Calculus for those who hate rational exponents"? But Cody was right on the last one--you can use it. Technically you always can, by letting u=<your independent variable.>

 

[galactus]

I agree with daon. There is really no need for a sub with these. But, if you have to..............

 

[lamaclass]

Oh ok well that's good to know! Just wanted to make sure I wasn't missing anything. Thanks a ton!