CLEP Calculus Review Problem #70

Hinzugefügt: 2026-06-04

[00:00:04]Number 70 is the last problem on the calculus exam guide. So let's get at it.

[00:00:10]Let f be a continuous function such that f ofx is greater than or equal to 0, meaning it's not negative on the interval from 0 to 2. f ofx is less than or equal to 0 on the interval 2 to 5.

[00:00:23]The integral from 0 to 2 of f ofx dx is 6. And the integral from 2 to 5 of f ofx dx is8. What is the value of the integral from 0 to 5 of f ofx plus the absolute value of f ofx dx? Using our properties of integrals, we can split this up as the integral from 0 to 5 of f ofx dx plus the integral from 0 to 5 of the absolute value of f ofx dx. Given that we've got an integral from 0 to 2 and 2 to 5 separately, it might be better to rewrite an integral from 0 to 5 of f ofx dx as the integral from 0 to 2 f ofx dx plus the integral of 2 to 5 f ofx dx. So I'm actually going to do that with both of these integrals. So the first one would be exactly what I wrote above. And I'll do basically the same thing with that next integral. Once we have it all separated out like this, we can just use the values that we're given. So the integral from 0 to 2 of f ofx dx is 6. The integral from 2 to 5 of f ofx dx is8. The integral from 0 to 2 of the absolute value of f ofx is also going to give us 6 because 6 is already positive. And when you take the absolute value of a positive number, it remains positive. Now, when we're trying to find the integral from 2 to 5 of the absolute value of f ofx dx, since the absolute value changes any negative values to positive, instead of getting 8, we're going to get positive 8. So, at this point, we just need to add up all of our numbers here. 8 - 8 is 0 and 6 + 6 is 12. Well, that about wraps up these 70 problems that are on the calculus exam guide. If you made it all the way to question 70, I got to give you major props because this is a lot of questions. But overall, thanks for watching and y'all have a great day.