Question

integral from x to (x^2) of (t^4)dt

Answer 1

\[\large \int\limits_x^{x^4}t^4\;dt\]

Simply apply the `Power Rule for Integration`.
~Increase the power on t by 1.
~Divide by this new power.

Answer 2

Can you figure that part out?
After that, we have to evaluate the function at the upper and lower limits of integration. :)

Answer 3

doesnt the t^4 become (t^5)/5

Answer 4

Yes good.

Answer 5

i am going to make a guess that you are asked to find the derivative of that thing
i may be wrong

Answer 6

Yah it looks like an FTC problem :p
But whatev :D

Answer 7

\[\large \color{royalblue}{\frac{1}{5}t^5}|_x^{x^4}\]So here the anti-derivative of our function we started with.
We now will plug in our upper boundary `x^4` and subtract from that, the function evaluated at the lower limit.\[\large \color{royalblue}{\frac{1}{5}t^5}|_x^{x^4} \quad = \quad \left(\color{royalblue}{\frac{1}{5}(x^4)^5}\right)-\left(\color{royalblue}{\frac{1}{5}(x)^5}\right)\]Understand what we did there Umbaka? :O

Answer 8

thanks, I know how to get the antiderivative but since it is asking for the derivative, does it become [(4(x^6))(2x)]-[4x^3]

Answer 9

Hmmm I think the derivative will give us this,
\[\large \frac{d}{dx}\left(\color{royalblue}{\frac{1}{5}x^{20}}\right)-\left(\color{royalblue}{\frac{1}{5}x^5}\right)\]
\[\large =4x^{19}-x^4\]

Answer 10

Thank you so much!

Answer 11

aren't you suppose to use the fundamental theorem of calculus?

Answer 12

Yes, but he didn't inform us that we were taking a derivative until we had already gone through most of the problem :) So we just finished it this way.