Question

show geometrically why the integral of sqrt(2-x^2) in the interval (0,1) is equal to
(pi/4)+(1/2)

Answer 1

http://www.wolframalpha.com/input/?_=1328164066711&i=+integral+of+sqrt(2-x%5e2)&fp=1&incTime=true

Answer 2

the function represents the upper half of a circle of radius sqrt2
at x=1, y =1, from unit circle we know that the angle is pi/4: tan pi/4 = y/x = 1
The area from 0 to 1 is the combined area of a 1/8 sector of circle plus a triangle of length and height of 1.