1. ## area between curves

x=y^2 + 2

y=0
y=3
x=0

find the area..

can anybody help me start this problem?

2. Originally Posted by FinalFantasy9291
x=y^2 + 2

y=0
y=3
x=0

find the area..

can anybody help me start this problem?
This is the area of the curve against the y-axis from y=0 to y=3
x=0 is the y-axis.

$\displaystyle \int_{y=0}^3f(y)dy=\int_{y=0}^3\left(y^2+2\right)d y$

3. Originally Posted by FinalFantasy9291
x=y^2 + 2

y=0
y=3
x=0

find the area..

can anybody help me start this problem?
This is a parabola in the XY plane and your bounds are given. So lets set this up

$\displaystyle \int_0^3 dy \int_0^{y^2 + 2} dx$

Where does this come from? Well we are bounded by the x function and the co-ordinate planes. So clearly, our dx integral is from 0-->function. Likewise, y is bounded by the co-ordinate axis and a function, but in this case that function is 3. Thus our bounds are from 0-->3

You can also switch the limits of integration here and compute dy first before dx.