Help evaluating Definite Integral

[Gameowner]

Homework Statement

Hi guys, need help evaluating this integral.

Integrate from -1 to 1

(t^i)(t^5-t^4) dt

Where i just an arbitrary variable, (it's actually an index number of a matrix)

Homework Equations

The Attempt at a Solution

So I thought I would begin by expanding the bracket to get

(t^(5+i))+(t^(4+i)) dt

then just evaluating it like you do

((t^(6+i))/(6+i))+((t^(5+i))/(5+i)) from -1 to 1

then just plugging the -1 and 1 into the t's, to get

((-2)^(6+i)/(6+i))+(2^(5+i)/(5+i))

 

[cryora]

Hmm, somehow the minus sign in the original problem turned into a plus when you expanded the expression.

I'm not sure how you got the -2 and 2 on the last part. Maybe you are adding the exponent bases together, but that doesn't work. 5^x + 5^x does not equal 10^x.

Integration using x^n = (n+1)x^(n+1) only works if n is not -1, otherwise the integral of (x^n)dx with n=-1 becomes ln(x). However, if this is the first semester of single variable calculus, then I suppose they want you to assume that the power is not -1 and just integrate with x^n = (n+1)x^(n+1).

 

[mathgeek4]

your attempt at the solution seems right to me.. as long as the variable i does not depend on t..
There are two errors (i) you have changed the minus sign from the original Integral to a + sign when you are actually evaluating it.
and when you plug the limits -1 and 1, you should get, ((-1)^(6+i))/(6+i)-(1/(6+i))-((-1)^(5+i))/(5+i)+(1/(5+i)).
you have plug the upper limit and the lower limit into each of the individual terms in the sum.

Hope this helps =)

 

[Gameowner]

Nope, this is a fourth year optimization course. This question came out of approximating a function using a polynomial which lead to all this matrix index integral evaluation.

Always seem to get tricked up with the simple calculus ><

Yes, you guys are right, I don't know why I typed + instead of minus, I have here on my working minus, typo...

I also realized where I gone wrong, yea I added the exponent bases together which I shouldn't have done, if I take all those errors I made. I should get the answer that mathgeek4 posted.

Thanks for all your help!