Question

if f(x)=integral of (-12sinx)/(cos^2 x) dx+c and f(0)=-4 find c

Answer 1

I think we will need to evaluate the integral first and then substitute x=0 and f(0) = -4.
Do you recognize the ability for u-substitution in that case?

Answer 2

can you solve this one for me please , i want use this one as example to solve other qoustion

Answer 3

We would first evaluate the integral.
Integral of -12 sin x / (cos ^2 x) dx
12 * integral of -sin x / (cos^2 x) dx U-substitution of u = cos x, du = - sin x dx
12 * integral of du / u^2
12 * integral of u^(-2) du Power rule and then back-substitute u = cos x.
12 * u^(-2 + 1) / (-2 + 1)
f(x) = 12 * (cos x)^(-2 + 1) / (-2 + 1) + c
Substitute x=0 and f(0) = -4 here, and the only variable remaining is c. You can see how you would solve for c from here?

Answer 4

thanks

Answer 5

You're welcome! :)

Answer 6

u r right