document.write( "Question 85525: f(x) = tan^-1(x) ... find the area bounded by [0,pi/4] using any technique \n" ); document.write( "

Algebra.Com's Answer #61760 by Nate(3500) $\"\"$ $\"About$

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A(x) = f'(x)
\n" ); document.write( " $\"+int%28+arctan%28x%29+%2C+dx+%2C+0+%2C+pi%2F4%29\"$
\n" ); document.write( "[u = arctan(x)
\n" ); document.write( "[du = dx/(1 + x^2)
\n" ); document.write( "[dv = dx
\n" ); document.write( "[v = x
\n" ); document.write( " $\"x%2Aarctan%28x%29+-+int%28+x%2F%281+%2B+x%5E2%29+%2C+dx+%2C+0+%2C+pi%2F4%29\"$
\n" ); document.write( "[u = 1 + x^2
\n" ); document.write( "[du = 2x dx
\n" ); document.write( " $\"x%2Aarctan%28x%29+-+int%28+x%2F%28u%29+%2C+du%2F2x+%2C+0+%2C+pi%2F4%29\"$
\n" ); document.write( " $\"x%2Aarctan%28x%29+-+%281%2F2%29%2Aint%28+1%2F%28u%29+%2C+du+%2C+0+%2C+pi%2F4%29\"$
\n" ); document.write( " $\"x%2Aarctan%28x%29+-+%281%2F2%29%2Aln%28u%29\"$ | $\"pi%2F4\"$ / 0
\n" ); document.write( " $\"x%2Aarctan%28x%29+-+%281%2F2%29%2Aln%281+%2B+x%5E2%29\"$ | $\"pi%2F4\"$ / 0
\n" ); document.write( "(pi/4)(arctan(pi/4) - (1/2)ln(1 + pi^2/16)
\n" ); document.write( "Aprox. 0.2827 \n" ); document.write( "

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