- #1

LearninDaMath

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## Homework Statement

Use Part 2 of the Fundamental Theorem of Calculus to find the derivative.

[tex] \int_3^x sin(t^{5}) \, dt [/tex]

## Homework Equations

## The Attempt at a Solution

I know the general idea of what I'm supposed to do as far as evaluate the indefinate integral and then do a subtraction of the upper limit and lower limits...but I can't even get to the point of finding the indefinate integral. (maybe it's that I just "think" I know what i'm supposed to do..)

[tex] \int_3^x sin(t^{5}) \, dt [/tex]

I'm letting u = [itex]t^{5}[/itex]

so du = [itex]5t^{4}[/itex]

then it looks like dt can be replaced by [itex]\frac{1}{5t^{4}}[/itex]

so that [tex] \int_3^x \frac{1}{5t^4} sin(u) \, du [/tex]

However, our professor has instructed that mixing variables within the integral is not allowed because it can't be evaluated.

So how to I do u-substitution on this integral?