8. Definite Integrals

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

${\lim }_{n\to \infty }{\sum }_{k=1}^n{(x_k^{\ast }-3)}^2\Delta x$

Find ${\int }_0^{6}f\left(x\right)dx$ given the graph of $y=f\left(x\right)$.

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.

${\int }_1^6\sqrt{x^2-5x}dx-{\int }_{10}^6\sqrt{x^2-5x}dx$

Evaluate the following definite integral.

${\int }_{100}^{100}\frac{\sin \left(2x\right)-100x^2}{\sqrt{x^5+\tan (3x-6)}}dx$