What is $f(x) = int x-x^2secx dx$ if $f(pi/4)=3$ ?

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Answer 1 · 2018-08-13T21:07:08

$int(x-x^2)dx=x^2/2-x^3/3+3+pi^3/192-pi^2/32$ if $f(pi/4)=3$

$I=int(x-x^2)dx$

$=intxdx-intx^2dx$

$=x^2/2-x^3/3+C$ , $C in RR$

Also, $f(pi/4)=3$

$(pi/4)^2/2-(pi/4)^3/3+C=3$

$C=3+pi^3/192-pi^2/32$

Finally, $I=x^2/2-x^3/3+3+pi^3/192-pi^2/32$

\0/ here's our answer !

What is f(x) = int x-x^2secx dxf(x) = int x-x^2secx dx if f(pi/4)=3 f(pi/4)=3 ?