# BC Calculus FTC Worksheet

• Class: 5H: BC Calculus
• Author: Peter Atlas
• Text: Calculus Finney, Demana, Waits, Kennedy

Find the following:

1. If $$F(x) = \displaystyle \int_{1}^{x} \frac{1}{1+t^2} \, dt$$, find $$F'(x)$$.
2. If $$F(x) = \displaystyle \int_{3}^{2x}\sqrt{t^2 + 1} \, dt$$, find $$F'(x)$$.
3. If $$F(x) = \displaystyle \int_{x}^{2x} \frac{1}{t} \, dt$$ for $$x > 0$$, find $$F'(x)$$.
4. If $$F(x) = \displaystyle \int_{0}^{\sqrt{x}} \sin{ \left(t^2 \right) } dt$$, find $$F'(x)$$.
5. If $$x > 0$$, then find $$\displaystyle \frac{d}{dx} \int_{1}^{\frac{1}{x}} \frac{2}{t} \ dt$$.
6. Find $$\displaystyle \int_{1}^{4} \frac{d}{dx} \sqrt{x^2 - 1} \, dx$$.