How to find the area of two simple figures to evaluate the integral from -3 to 0

[synergix]

Homework Statement

Evaluate the integral by intrepreting it in terms of areas

from -3 to 0

(1+ sqrt(9-x²)dx

Homework Equations

integral = F(0)-F(-3)

The Attempt at a Solution

first find F

F = x - [(9-x²)^3/2]/3

I solved using integral = F(0)-F(-3)

and I got the incorrect answer I think it is because I am finding the definite integral and not the area. If this was my problem how would I find the area? Graphing?

 

[Mark44]

Yes - graph it. The function defines a fairly simple geometric object.

BTW, your work finding an antiderivative, besides not being the direction you're supposed to go, is incorrect. If you take the derivative of the function you found, you don't get 1 + sqrt(9 -x^2)

 

[synergix]

ok i changed it i think its right now and i will try to graph it

 

[Mark44]

If you want to get credit for your work, the first thing you should do is graph your function. This problem has nothing to do with finding antiderivatives.

 

[HallsofIvy]

It would help to think of this as two separate integrals:
$$\int_{-3}^0 1+ \sqrt{9- x^2} dx= \int_{-3}^0 1 dx+ \int_{-3}^0 \sqrt{9- x^2} dx$$
Graph each, if necessary, to recognise that those are simple figures and use basic area formulas.