Factors of 12 : 1, 2, 3, 4, 6, 12
Factors of 20: 1, 2, 4, 5, 10, 20
In both lists of factors, 4 is in common. Therefore, the value of K is 4 because it can divide into both 12 and 20 without a remainder. 2 is also another possible value of K.
We're looking for the two values being subtracted here. One of these values is easy to find:
<span>g(1) = ∫f(t)dt = 0</span><span>
since taking the integral over an interval of length 0 is 0.
The other value we find by taking a Left Riemann Sum, which means that we divide the interval [1,15] into the intervals listed above and find the area of rectangles over those regions:
</span><span>Each integral breaks down like so:
(3-1)*f(1)=4
(6-3)*f(3)=9
(10-6)*f(6)=16
(15-10)*f(10)=10.
So, the sum of all these integrals is 39, which means g(15)=39.
Then, g(15)-g(1)=39-0=39.
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I hope my answer has come to your help. God bless and have a nice day ahead!
