Evaluate the definite integral ${\int }_0^{1}1+7xdx$.

Lifetime of a tire Assume the random variable L in Example 2f is normally distributed with mean μ = 22,000 miles and σ = 4,000 miles.

a. In a batch of 4000 tires, how many can be expected to last for at least 18,000 miles?

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 $[0,10]$.

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

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.

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