Answer
Explanation
Given:
A bug is moving along a straight path with velocity
[tex]V(t)=t^2-6t+8\text{ }for\text{ }t>0[/tex]What to find:
The total distance traveled by the bug over interval [0, 6].
Solution:
To find the total distance traveled by the bug over interval [0, 6], you first integrate v(t)= t² - 6t + 8
[tex]\begin{gathered} \int_0^6t^2-6t+8 \\ \\ [\frac{t^3}{3}-\frac{6t^2}{2}+8t]^6_0 \\ \\ (\frac{t^3}{3}-3t^2+8t)^6-(\frac{t^{3}}{3}-3t^2+8t)^0 \\ \\ (\frac{6^3}{3}-3(6)^2+8(6))-(\frac{0^3}{3}-3(0)^2+8(0)) \\ \\ (\frac{216}{3}-3(36)+48)-(0-0+0) \\ \\ 72-108+48-0 \\ \\ =12\text{ }units \end{gathered}[/tex]