Indefinite Integrals

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ifailedcalculus

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Apr 2, 2009
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Hey guys I don't really have a firm grasp on Indefinite Integrals.

First I don't even know the difference between Definite and Indefinite Integrals

I have a few math assignments, if anyone can show me or tell me some step by step ways to solve the problem it would be really great.

Here is the first question to my assignment, if i get it, i should be able to do the rest on my own, hopefully.

?x^4*e^(x^5) dx

what I got was

1/5*e^(x^5)

obviously its wrong..

thanks for your help
 
ifailedcalculus said:
Hey guys I don't really have a firm grasp on Indefinite Integrals.

First I don't even know the difference between Definite and Indefinite Integrals

I have a few math assignments, if anyone can show me or tell me some step by step ways to solve the problem it would be really great.

Here is the first question to my assignment, if i get it, i should be able to do the rest on my own, hopefully.

?x^4*e^(x^5) dx

what I got was

1/5*e^(x^5)

Why do you think this is wrong?

One way to check the answer for indefinite integral is to find the derivative of your calculated answer (differentiate).

That might also give the direction to get it correct.

Remember to add 'C' after every indefinite integral.

obviously its wrong..

thanks for your help
Click to expand...
 
Hi, a good one to practice my tex.

\(\displaystyle \int x^{4}e^{x^{5}}dx\) \(\displaystyle Let \ u \ = \ x^{5}, \ then \ du = 5x^{4}dx.\)

\(\displaystyle Ergo \ \int x^{4}e^{x^{5}}dx = \int \frac{e^{u}}{5}du = \frac{e^{u}}{5} \ +C = \frac{e^{x^{5}}}{5} + C\)

Note: This is an indefinite integral, a definite integral is a number, whereas an indefinite integral is a family of functions, in this case the family of functions is \(\displaystyle f(x) = \frac{e^{x^{5}}}{5} + C.\)
 
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