# One last problem

1. Dec 11, 2003

### tandoorichicken

I think Mr. Gishe went trigger happy when he was assigning homework today.

$$y=\sqrt{a^2-x^2}$$ where -a<=x<=a is a semicircle with r=a
show why $$\int_{-a}^{a} \sqrt{a^2-x^2}\,dx = \frac{1}{2} \pi a^2$$

(I think that's how its written)

2. Dec 11, 2003

### StephenPrivitera

What does the integral represent if the integrand is positive!!??? AREA!!!!!!!
What's the area of a half circle?

3. Dec 12, 2003

### himanshu121

It is given in the que it is a semi-circle
Do you know the area of circle
if yes then u can find the area of semicircle

or if u dont know n u want to calulate the integral

substitute
x=asinz