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Numerade Educator

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Problem 50 Medium Difficulty

Find $ \displaystyle \int^5_0 f(x) \, dx $ if

$ f(x) = \left\{
\begin{array}{ll}
3 & \mbox{if $ x < 3 $}\\
x & \mbox{if $ x \ge 3 $}
\end{array} \right.$

Answer

17

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Video Transcript

we have the integral from 0 to 5 and three is the height from 0 to 3. And then why equals X is the height from three and beyond. Then we want to find the area under the two curves. So the area under this rectangle here would just be three times three or nine and the area under this blue. Why, it was X line there. It's going to be what we could do this with a trapezoid, Um, and so that would end up being a base of two. Actually, you know, let's just do a rectangle on the triangle instead. So that would be two times three. So that would be an area of six there, and then that would be a height of two with of 22 times 24 divided by two. So that would be in the area of two up top. So just so you can see both of those, that's to that six. And that's of course, our first nine. So the total area under the curve there is going to be 17 9 plus six plus two. Therefore, that's what the Senate girl evaluates dio