8. Definite Integrals

Find $\int_0^6\!f\left(x\right)\,dx$ given the graph of $y=f\left(x\right)$.

Express the following limit as a definite integral on the interval $[0,10]$.

$\lim_{n\to\infty}\sum_{k=1}^{n}\left(x_{k}^{\ast}-3\right)^2\Delta x$

Given the following definite integral of the function $f\left(x\right)=3x^2-2x$, write the simplified integral:

-$\int_4^0\!f\left(x\right)\,dx$

Write the two definite integrals subtracted below as a single integral.

$\int_1^6\!\sqrt{x^2-5x}\,dx-\int_{10}^6\!\sqrt{x^2-5x}\,dx$