What is f(x) = int x^2sinx^3 + 6cosx dx if f(pi/12)=-8 ?

1 Answer
Feb 26, 2018

f(x) = -1/3 cos((pi/12)^3)+6 sin (pi/12)-9.22

Explanation:

f(x) = int x^2 sin(x^3) dx+ int 6 cos x dx
= 1/3 int sin(x^3) times 3x^2 dx +6 sin x
= 1/3 int sin(x^3) d(x^3) +6 sin x
= -1/3 cos(x^3)+6 sin x +C

We can find C from the given condition f(pi/12)=-8

-8 = f(pi/12) = -1/3 cos((pi/12)^3)+6 sin (pi/12) +C

so

C = 1/3 cos((pi/12)^3)-6 sin (pi/12)-8 ~~-9.22

and thus
f(x) = -1/3 cos((pi/12)^3)+6 sin (pi/12)-9.22