SOLUTION: f(x) = tan^-1(x) ... find the area bounded by [0,pi/4] using any technique

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Question 85525: f(x) = tan^-1(x) ... find the area bounded by [0,pi/4] using any technique
Answer by Nate(3500) About Me  (Show Source):
You can put this solution on YOUR website!
A(x) = f'(x)
+int%28+arctan%28x%29+%2C+dx+%2C+0+%2C+pi%2F4%29
[u = arctan(x)
[du = dx/(1 + x^2)
[dv = dx
[v = x
x%2Aarctan%28x%29+-+int%28+x%2F%281+%2B+x%5E2%29+%2C+dx+%2C+0+%2C+pi%2F4%29
[u = 1 + x^2
[du = 2x dx
x%2Aarctan%28x%29+-+int%28+x%2F%28u%29+%2C+du%2F2x+%2C+0+%2C+pi%2F4%29
x%2Aarctan%28x%29+-+%281%2F2%29%2Aint%28+1%2F%28u%29+%2C+du+%2C+0+%2C+pi%2F4%29
x%2Aarctan%28x%29+-+%281%2F2%29%2Aln%28u%29 | pi%2F4 / 0
x%2Aarctan%28x%29+-+%281%2F2%29%2Aln%281+%2B+x%5E2%29 | pi%2F4 / 0
(pi/4)(arctan(pi/4) - (1/2)ln(1 + pi^2/16)
Aprox. 0.2827