How can we find the exact integral of a circle? For example, Intregral from -3 to 0 of f(x) = (1 + sqrt(9 - x^2) ) dx ? Thank you ^^

Question

anonymous · Answer

Do you mean Area of Circle through Integration?

anonymous · Answer

They want is to find the area under the curve on those conditions, the book approach is to find the area of 1/4 circle, and then just use a rectangle to estimate the area below the 1/4 circle... that would be only an approximation, I would like to see how I can find teh actualy value. My calculator can't do it either.

anonymous · Answer

$$\int\limits_{-3}^{0} 1 + \sqrt{9-x^2}$$

anonymous · Answer

You don't need integration here.  The radius of the circle is three.  Therefore the area of the circle is pi*9.  Then just divide by 4.  Voila, area of 1/4th of the circle.

anonymous · Answer

Actually, you do need integration because of the vertical shift.

precal · Answer

Remember integration is area under a curve, if you notice part of the graph is a circle
use the area of the circle formula from geometry.  If it is a semicircle divide it by 2, If it is a quarter of a circle , divide it by 4.