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Problem 3 Evaluate the integral expression below, where a ( x ) and b ( x ) are both piece - wise functions shown in
Problem
Evaluate the integral expression below, where and are both piecewise functions shown in the provided figures below.
Hint: You should get as your final answer. If you are unsure of where to start or get stuck, consider the following:
An integral can be calculated as the area under a curve. This may help you get the denominator of the desired expression hint: the denominator should be
To tackle the numerator, consider applying the additive properties of definite integrals:
This problem is easiest to solve if you break up the numerator on the intervals of and Then, remember the integral constant multiple rule, where if is constant with respect to on the given interval between and you can factor it out of an integral as:
Using these two integral properties combined with the areaunderacurve principle you can solve for the numerator. hint: the numerator should be
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