first of all reduce the equation to simplest form:
y = 2√x
y = 5
y + 2x = 4
Your sketch should look like a "triangle" with one side slightly curved
see:
http://www.wolframalpha.com/input/?i=plot+y%3D2*sqrt%28x%29+%2C+y%3D5+%2C+y%2B2x%3D4
we need all the intersection points,
I assume you know how to do that, ....
but I will do the hardest one:
intersect y = 2√x and y + 2x = 4
then 2√x = (4-2x)
or
√x = 2-x
by inspection, x = 1 , then in the originals , y = 2
point of intersection is (1,2)
Hoping that you get (-1/2, 5) and ( 25/4,5) for the other points
so area
= ∫(5 - (4-2x)) dx from -1/2 to 1 + ∫(5 - 2x^(1/2) dx from 1 to 25/4
= (x + x^2)| from -1/2 to 1 + (5x - 4x^(-1/2) )| from 1 to 25/4
= 1 + 1 - (-1/2 + 1/4) + (125/4 - 8/5 - (5-4) )
= 2 + 1/4 + 125/4 - 8/5 - 1
= 309/10
you better check my arithmetic on that one, should have written it out on paper first.
Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y. Then find the area of the region.
2y=4*sqrt(x) , y=5 and 2y+4x=8
please help! i've been trying this problem the last couple days, even asked a TA for help, but i can't arrive at the right area between the curves. Thanks in advance!
2 answers
Thanks I figured it out my answer was 9, and it was correct