Asked by can somebody explain how to do it?
find the area enclosed by the given curves.
y=squareroot of x
y=x/2
x=9
* i just graph it but do not know how to set it up the equation or anything.
y=squareroot of x
y=x/2
x=9
* i just graph it but do not know how to set it up the equation or anything.
Answers
Answered by
Steve
I think there's a typo here. The curves intersect at (0,0) and (4,2). Going out to x=9 is bogus, unless you want to add up two areas.
Think of the area as a lot of small rectangle, each of width dx and height the distance between the curves.
a = ∫[0,4] √x - x/2 dx
a = 2/3 x^3/2 - 1/4 x^2 [0,4]
= (2/3 * 8 - 1/4 * 16)-(0)
= 16/3 - 4
= 4/3
If you really want to go out to x=9, then add the area, swapping which curve is on top:
add on ∫[4,9] x/2 -√x dx
Think of the area as a lot of small rectangle, each of width dx and height the distance between the curves.
a = ∫[0,4] √x - x/2 dx
a = 2/3 x^3/2 - 1/4 x^2 [0,4]
= (2/3 * 8 - 1/4 * 16)-(0)
= 16/3 - 4
= 4/3
If you really want to go out to x=9, then add the area, swapping which curve is on top:
add on ∫[4,9] x/2 -√x dx
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