Derivative of this interval?

[SRB]

Hey there! This is what the question reads:

Use the FTC (Fundamental Theory of Calculus) to find F', given F= sqrt(1+r³)dr, I'm not sure how to make the interval symbol, but on top is 0 and below is x².

What I did so far is flip flopped the 0 and x² and made the rest of the function negative and then im stuck

 

[tkhunny]

"Interval" symbol? Do you mean integral symbol?

If you could find the antiderivative of sqrt(1+r^{2}), what would you do with it?

Hint:

Let's suppose that h(t) = H'(t). Then: \(\displaystyle \int_{0}^{x} h(t)\;dt = H(x) - H(0)\)

Further: \(\displaystyle \frac{d}{dx}\left[\int_{0}^{x} h(t)\;dt\right] = \frac{d}{dx}\left[H(x) - H(0)\right] = H'(x) = h(x)\)

Let's see what you get.

 

[HallsofIvy]

Hey there! This is what the question reads:

Use the FTC (Fundamental Theory of Calculus) to find F', given F= sqrt(1+r³)dr, I'm not sure how to make the interval symbol, but on top is 0 and below is x².

What I did so far is flip flopped the 0 and x² and made the rest of the function negative and then im stuck

Yes, \(\displaystyle \int_x^0 f(t)dt= -\int_0^x f(t)dt\)
Now, the problem says "Use the FTC" so what does the FTC say?