Use ${\displaystyle \underset{0}{\overset{10}{}}}g(u)du=3$ to answer the questions below.

$($a$)$ In this part, you will use the method of substitution to evaluate ${\displaystyle \underset{0}{\overset{100}{}}}g(\frac{t}{10})dt.$

What substitution would be appropriate so that you can use the given information?

$u=$

Use your substitution to rewrite the integral in terms of $u$ only, and then evaluate it$.$

${\displaystyle \underset{0}{\overset{100}{}}}g(\frac{t}{10})dt$

$={\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}|du||$

$($b$)$ In this part, you will use the method of substitution to evaluate ${\displaystyle \underset{0}{\overset{10}{}}}g(10-t)dt.$

What substitution would be appropriate so that you can use the given information?

$u=$

Use your substitution to rewrite the integral in terms of $u$ only, and then evaluate it$.$ Write your integral so that your lower endpoint is smaller than the upper endpoint. ${\displaystyle \underset{0}{\overset{10}{}}}g(10-t)dt$

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