# How do you find the area bounded by #y=4-x^2#, the x and y axis, and x=1?

##### 1 Answer

Dec 4, 2016

First picture what this region would look like by envisioning its graph (or just looking straight at it):

graph{4-x^2 [-9.54, 10.46, -3.92, 6.08]}

Thinking about how this is bounded from side to side, we see it's bounded by the

Since it's also bounded by the

graph{(4-x^2)sqrt(x-x^2)/sqrt(x-x^2) [-2, 3, -1, 4.72]}

This are can be found through integrating the function from

#int_0^1(4-x^2)dx#

Integrating (finding the antiderivative) and keeping the bounds gives:

#=[4x-x^3/3]_0^1#

#=[4(1)-1^3/3]-[4(0)-0^3/3]#

#=(4-1/3)-(0-0)#

#=11/3#

The area under the specified curve with the specified bounds is