What is #F(x) = int sin(3x)-sinxcos^2(4x) dx# if #F(pi) = 3 #? Calculus Techniques of Integration Evaluating the Constant of Integration 1 Answer Monzur R. Apr 28, 2017 #F(x) =1/2cosx-1/3cos3x-1/28cos7x+1/36cos9x+199/63# Explanation: #F(x) = int sin3x - sinxcos^2(4x)dx=# #1/2cosx-1/3cos3x-1/28cos7x+1/36cos9x+"c"# #F(pi)= -10/63 + "c"=3# #"c"=199/63# #F(x) =1/2cosx-1/3cos3x-1/28cos7x+1/36cos9x+199/63# Answer link Related questions How do you find the constant of integration for #intf'(x)dx# if #f(2)=1#? What is a line integral? What is #f(x) = int x^3-x# if #f(2)=4 #? What is #f(x) = int x^2+x-3# if #f(2)=3 #? What is #f(x) = int xe^x# if #f(2)=3 #? What is #f(x) = int x - 3 # if #f(2)=3 #? What is #f(x) = int x^2 - 3x # if #f(2)=1 #? What is #f(x) = int 1/x # if #f(2)=1 #? What is #f(x) = int 1/(x+3) # if #f(2)=1 #? What is #f(x) = int 1/(x^2+3) # if #f(2)=1 #? See all questions in Evaluating the Constant of Integration Impact of this question 1186 views around the world You can reuse this answer Creative Commons License