Question

Find the total distance traveled during the first 8s for v = 3t^2 - 24t + 36

Answer 1

Velocity is the derivative of distance, so integrate:

$v = 3t ^{2} - 24t + 36$

And input 8 for t.

Find

$\int\limits_{0}^{8} (3t^2 - 24t + 36) dt \\ \\t^3|^8_0-12t^2|_0^8+36t|_0^8 \\ \\8^3-0^3-12(8^2-0^2)+36(8-0) \\512-768+288 \\32$