Let f(x) = √(1-x²)
Find the definite integral
of f(x) between x = 0 and x = 1
The definite integral of f(x) between x=0 and x=t can be evaluated as
(1/2)[arcsin(t)+t*sqrt(1-t^2)]
using elementary integration techniques and trig identities. First
making the substitution x=sin(u) changes the integral to that of
[cos(u)]^2=(1/2)[1+cos(2u)] from u=0 to u=arcsin(t) from which the
result follows readily upon using the double angle formula for the sine.
Setting t=1 then yields PI/4 as the answer to the original problem.
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Posted by Richard
on 2006-08-26 13:17:33 |
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