Which of the following integrals represents the area of the region bounded by the curves $y=x^2$ and $y=4$ between $x=0$ and $x=2$?

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

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

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.

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

Which of the following limits is equal to the definite integral from $2$ to $5$ of $1+x^4$ $dx$?

Which of the following definite integrals are equal to $0$?

Which of the following definite integrals is equal to the area under the curve $y=x^2$ from $x=0$ to $x=2$?

What is the average (mean) value of the function $3t^3-t^2$ over the interval $1\le t\le 2$?