how do you find the area of semi circle using the equation ; integral from -10 to 10 (1/2)(pi)(r squared)(dx)?
Integral represent area below the curve. Since the boundaries of integral are -10 and 10, radius of the circle is 10 and center is (0,0). Thus, equation of circle is
Now, integral represents area below the curve. To find area of semicircle, we have to express y as a function of x and integrate from -10 to 10.
We take only positive values because we can take upper half of circle.
If we evaluate area of circle with radius r=10 result is 100π, so area of half circle is 50π.