My Math Forum Solving for indefinite integral

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 March 19th, 2009, 01:58 AM #1 Newbie   Joined: Mar 2009 Posts: 3 Thanks: 0 Solving for indefinite integral My daughter at college asked me to help her with these but it's been years since I've done them. I said I would try and then look over what she comes up with so any help would be great not so I can give her the answers but so I can tell her whether or not she on the right track and help her try to find it! Problem 1 ?(t^3/2 + 2t^1/2 -4t^-1/2)dt= ?t^3/2(dt) + 2?t^1/2(dt) -4?t^-1/2(dt)= 2/3t^5/2 +(2)(2)t^3/2 -(4)(2)t^1/2 +c= 2/3t^5/2+4t^3/2-8t^1/2+c Am I anywhere near right with this one? And the second one is: ?sqrt(t)(t^2+t-1)dt but I have no idea where to go with it... Thanks to any and all that help and for any help you can give.
March 19th, 2009, 02:48 AM   #2
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Re: Solving for indefinite integral

Quote:
 Originally Posted by 4littlepiggiesmom Problem 1 ?(t^3/2 + 2t^1/2 -4t^-1/2)dt= ?t^3/2(dt) + 2?t^1/2(dt) -4?t^-1/2(dt)= 2/3t^5/2 +(2)(2)t^3/2 -(4)(2)t^1/2 +c= 2/3t^5/2+4t^3/2-8t^1/2+c And the second one is: ?sqrt(t)(t^2+t-1)dt
Problem 1

Break it up into three separate integrals and factor out the constants.

$\int t^{\frac{3}{2}}+2t^{\frac{1}{2}}-4t^{-\frac{1}{2}}dt\mbox{ }=\mbox{ }\int t^{\frac{3}{2}}dt\mbox{ }+\mbox{ }2\int t^{\frac{1}{2}}dt\mbox{ }-\mbox{ } 4\int t^{-\frac{1}{2}}dt$

Use $\frac{1}{n+1}t^{n+1}$ where n is the original exponent then multiply by the constant outside of the integral to get:

$\frac{2}{5}t^{\frac{5}{2}}+\frac{4}{3}t^{\frac{3}{ 2}}-8t^{\frac{1}{2}}+C$

the second one

$\int \sqrt{t}(t^2+t-1)dt\mbox{ }=\mbox{ }\int t^{\frac{1}{2}}(t^2+t-1)dt\mbox{ }=\mbox{ }\int t^{\frac{5}{2}}+t^{\frac{3}{2}}-t^{\frac{1}{2}}dt$

$=\mbox{ }\frac{2}{7}t^{\frac{7}{2}}\mbox{ }+\mbox{ }\frac{2}{5}t^{\frac{5}{2}}\mbox{ }-\mbox{ }\frac{2}{3}t^{\frac{3}{2}}\mbox{ }+\mbox{ }C$

 March 19th, 2009, 05:20 AM #3 Newbie   Joined: Mar 2009 Posts: 3 Thanks: 0 Re: Solving for indefinite integral Thank you I knew after working some more I had to add on the second one but wasn't sure where it fit in!

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