What is f(x) = int x-sin2x-6cosx dx if f(pi/2)=3 ?

1 Answer
Dec 22, 2016

f(x)=x^2/2+1/2cos2x-6sinx+7/2-pi^2/8

Explanation:

f(x)=int(x-sin2x-6cosx)dx" "f(pi/2)=3

integrate term by term

f(x)=x^2/2+1/2cos2x-6sinx+C

f(pi/2)=1/2xx(pi/2)^2+1/2cos(2xxpi/2)-6sin(2xxpi/2)+C=3

pi^2/8+1/2cancel(cospi)^-1- 6cancel(sinpi)^0+C=3

pi^2/8-1/2+C=3

C=3+1/2-pi^2/8=7/2-pi^2/8

f(x)=x^2/2+1/2cos2x-6sinx+7/2-pi^2/8