SOLUTION: Find the area under the split-domain function from x = -2 to x = 3. f(x)= {7-x^2, (x<0) ......{7 , (x>= 0) have the graph but having trouble setting up can someone help

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: Find the area under the split-domain function from x = -2 to x = 3. f(x)= {7-x^2, (x<0) ......{7 , (x>= 0) have the graph but having trouble setting up can someone help       Log On


   

Question 203769: Find the area under the split-domain function from x = -2 to x = 3.
f(x)= {7-x^2, (x<0)
......{7 , (x>= 0)
have the graph but having trouble setting up can someone help please
thanks
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
If you have the graphs, then you know that to the right of the y-axisthe graph is simply a horizontal line. The area between it and the x-axis is just a rectangle whose area is 3*7 = 21.
The graph to the left of the y-axis is the left half of parabola which opens downward. At the moment, the only way I can think of to find the area between it and the x-axis is to use Calculus. If you don't know Calculus, then I hope someone else solves this problem for you.

The following integral will find the area in question:
int%28%287+-+x%5E2%29%2C+dx%2C+-2%2C+0%29+=+7x+-+%28%28x%5E3%29%2F3%29%29 evaluated from -2 to 0:
%287%280%29+-+%28%280%29%5E3%29%2F3%29+-+%287%28-2%29+-+%28%28-2%29%5E3%29%2F3%29%29
0+-+%28-14+-+%28-8%29%2F3%29
0+-+%28-14+%2B+8%2F3%29
0+-+%28-11%261%2F3%29
11%261%2F3
So the total area between the graph of f(x) from x = -2 to x = 3 is the sum of these areas: 21+%2B+11%261%2F3+=+32%261%2F3%29