Calculus - finding area help.

Question

anonymous · Answer

attachment

amistre64 · Answer

you simply have to define 2 intervals

amistre64 · Answer

edit***

what two functions do you play with from 0 to 7?  

and what two functions do you play with from 7 to 14?

anonymous · Answer

from 0 to 7 you are working with y=x and y= x^2/28

amistre64 · Answer

then find the integration from 0 to 7 of the difference between x^2/28 and x

amistre64 · Answer

$$\int_{0}^{7}(\frac{1}{28}x^2)-(x)~dx$$
area will always be a positive value in this case, so ignore any sign you get at the end

amistre64 · Answer

same concept for the 7 to 14 interval

anonymous · Answer

so I got -245/12 for the area of finding the integration from 0-7 of the difference between x^2/28 and x.... so it's positive 245/12

amistre64 · Answer

yes, so long as you did the actual integrating correctly

anonymous · Answer

for 7 to 14 would it be $$\int\limits_{7}^{14} (x^2/28)-(7) dx?$$

amistre64 · Answer

correct

amistre64 · Answer

there are of course other ways to view this, but that is the most fundamental view

anonymous · Answer

okay then afterwards i would subtract the answers to find the area between the regions.

amistre64 · Answer

we could have done;  x^2/28 - x  from 0 to 14,  then subracted x-7 from 7 to 14

amistre64 · Answer

no, add the areas to find the total area

amistre64 · Answer

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