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

1 Answer
Aug 13, 2018

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

Explanation:

#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 !