Integral Calculus

[rhyso88]

Hey, I was wondering if anyone could elighten me as to the method of approaching this integral, so far I have used a combination of Integration by parts and simple substitution, but the problem seems to go on forever!!!

∫ x ^ 3 dx / √ ( 3 + x ^ 2)

Any help would be greatly appreciated! I have been trying for ages[/tex][/i][/list]

 

[galactus]

Let \(\displaystyle u=3+x^{2}\), \(\displaystyle du=2xdx\), \(\displaystyle \frac{du}{2}=xdx\), \(\displaystyle u-3=x^{2}\)

\(\displaystyle \L\\\int\frac{x(x^{2})}{\sqrt{3+x^{2}}}dx\)

Now, you can take it from there, can't you?.

 

[rhyso88]

Intergals

Thanks very much, I never realised just how much you can substitute into the intergal and never thought to take the factor of X^3, thanks again

 

[rhyso88]

Just wanted to verify, I get the answer correct, but is it okay to end up with a final answer of ((u-3)(√u)-((2u^(3/2))/3 + C (because I forgot to put in that it was a definite integral bound by 0 to 1- but I can easily substitue these values and the answer is correct, what I did was use the values you presented, substituted them into the eq^n so everything in terms of U, then the integral of this required integration by parts. I just wanted to make sure that it is supposed to take that long and that I am not doing something stupid!

 

[galactus]

Using the substitution, you should get:

\(\displaystyle \L\\\int_{0}^{1}\frac{x(x^{2})}{\sqrt{3+x^{2}}}dx=\frac{1}{2}\int_{3}^{4}\frac{u-3}{\sqrt{u}}du\)

Subbing in your 0 and 1 into \(\displaystyle 3+x^{2}\) gives the limits 3 and 4. See?.

The \(\displaystyle \frac{1}{2}du\) takes care of the xdx

 

[rhyso88]

Thanks very much for your help, and yes I got the same answer as you by changing the limits, but I just wanted to verify it, once again thnks

 

[Guest]

calculus

the following table shows the rate of fuel consumption R(t) of an airplance at various times t. The airplane was observed for 80 min.

t (min) R(t)(gallons/min)
0 20
30 30
40 50
50 80
60 100
70 90

1. sketch a graph of R(t) versus t. Connect the points to form a smooth curve (without jagged edges).
2. Estimate R'(45). Explain how you got your answer.
3. Estimate R''(45). Explain how you got your answer.
4. Estimate the total amount of fuel consumed during the 70 minutes by using the values in the table. Explain how you got your answer
5. Explain the meaning of integral 50 on top and 30 bottom(sorry dont know how to use symbols yet) R(t)dt. Estimate the value of the integral by using the values in the table.[/list][/quote]

 

[stapel]

Re: calculus

the following table shows....

Please post new questions as new posts, not as "hijacks" of other students' posts.

Thank you for your consideration.

Eliz.