The Second Fundamental Theorem of Calculus Worksheet with Answer Key

What's on the worksheet

1. Evaluate each integral with the second fundamental theorem.
   \displaystyle\int_1^3 \left(6x^2 - 4x + 1\right)dx\displaystyle\int_4^9 \left(3\sqrt{x} - \dfrac{1}{\sqrt{x}}\right)dx\displaystyle\int_1^2 \left(\dfrac{4}{x^3} + x\right)dx\displaystyle\int_{-2}^{0} (x + 1)(x - 3)\,dx
2. Evaluate each integral exactly.
   \displaystyle\int_0^{\pi/3} \left(\sec x\tan x + 3\sin x\right)dx\displaystyle\int_0^{\ln 2} 6e^{3x}\,dx\displaystyle\int_{-e^2}^{-e} \left(\dfrac{4}{x} + 1\right)dx\displaystyle\int_{-\sqrt{3}}^{1} \dfrac{6}{1 + x^2}\,dx
3. Split each integral at its break.
4. Aisha's robotic lawn mower runs back and forth along a straight hedge.
5. Check each piece of work.