Question

Find the number a such that the line x = a divides the region bounded by the curves y = x, y = 0, and x = 4 into two regions with equal area.

Answer 1

I find it helps to graph what we are talking about.

Answer 2

area fromx= 0 to a =area fromx= a to 4

Answer 3

\[\int\limits_{o}^{a}y dx=\int\limits_{a}^{4}y dx\]
\[\int\limits_{0}^{a}x dx=\int\limits_{a}^{4}x dx\]
complete it

Answer 4

I got a=2sqrt(2)
=2.828

Answer 5

How would you go about checking y our result? Such a check would be pretty straightforward.

Answer 6

\[a=2\sqrt{2}\] is exact.
but decimal is approximate

Answer 7

Yes. Now, if you use this a as the upper limit of your first definite integral, and as the lower limit of your second, you could calculate a numerical answer (an area, by the way) for each integral. Are the 2 resulting def. ints. equal to one another?

I agree that 2Sqrt(2) is "exact" and as such is a better answer than "2.828."

Answer 8

the directions told me to give my answer to 3 decimal places so

Answer 9

thank you!

Answer 10

yw