# Thread: antiderivative of sine^t dt

1. ## antiderivative of sine^t dt

y= (from 0 to lnx) sin e^t dt

i know that you do u subsitution but I am confused with the sin...

2. are you really asked to compute the antiderivative, or the derivative?

3. antiderivative

4. no closed form for that one.

the reason i asked to you if you need to compute its derivative, it's because the upper bound is a function and the lower bound is a constant, then it calls to apply the Fundamental Theorem of Calculus.

5. Originally Posted by genlovesmusic09
y= (from 0 to lnx) sin e^t dt

i know that you do u subsitution but I am confused with the sin...
from 0 to lnx...

6. Originally Posted by genlovesmusic09
from 0 to lnx...
As has already been said, there is no closed form for the integral. Are you absolutely sure that the question does not ask you to find dy/dx?

7. (Excuse me for using the hiatus to jump in with a diagram!)

Just in case a picture helps, and you (or anyone) do want dy/dx here...

The fundamental theorem plus chain rule implies...

... where

... is the chain rule. (Straight continuous lines differentiate downwards with respect to x, and the straight dashed line similarly but with respect to the dashed balloon expression (which is the inner function of the composite, which is subject to the chain rule).

So we have...

...with one blank to fill in, and an obvious simplification.

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