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 Pre-Calculus and Calculus
 help with 2 intergration problems
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ep6
Junior Member

USA
4 Posts

Posted - 09/27/2007 :  19:43:37  Show Profile
i have what seems to be two simple intergration problems but I cannot get the answer that the book says it is. I will first give the problems and what I got and see what you guys get and see what the book says

the first problem is

(x^-(1/2))/x^(4/3) dx
when I solve this i get x^(11/6)dx so that equals
(-6x^(-5/6))/5 am I correct?

the second problem is

[(2/3 x^(3/2))(-x^(-1/2)]/4x^3 dx when i solve this i get
8/3 x^(-4/2) dx so that equals 8x^(-1)/-3

Now both of those answers are incorrect accoring to my book. I know I make a lot of mistakes in these kind of problems. Can anyone tell me what I did wrong?

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tkhunny
Advanced Member

USA
1001 Posts

Posted - 09/27/2007 :  23:27:02  Show Profile
[x^(-1/2)]/[x^(4/3)]

[x^(-3/6)]/[x^(8/6)]

[x^(-11/6)] <== You missed a sign, but it doesn't seem to have mattered.

Somehow, you managed to get it right, anyway.

Good work and be more careful.
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ep6
Junior Member

USA
4 Posts

Posted - 09/27/2007 :  23:37:22  Show Profile
so is my intergration done right for the first problem?
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tkhunny
Advanced Member

USA
1001 Posts

Posted - 09/28/2007 :  08:25:58  Show Profile
This is where I start to get nervous.

1) You do it right in the first place.
2) You can't tell that it's right.
3) Someone tells you that it's right.
4) You STILL don't know that it's right.

Please gain some self confidence. Please learn to evaluate your work. Did you make any errors? Are you able to review your steps? Check all your signs and arithmetic.

You look at the second one and you tell me if it's right.
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Subhotosh Khan
Advanced Member

USA
9117 Posts

Posted - 09/28/2007 :  10:14:14  Show Profile
How can you tell whether you have derived the correct anti-derivative of a function?

You find the derivative of your answer.

If the derivative is same as the original function - assuming you have done your differentiation correctly - you have found the correct anti-derivative.

Using the principles above - tell us whether you have done the second problem correctly - or not.

I understand your confusion - the book said you were wrong - however, books have been known to be wrong.
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