Question

Let F(x) be an antiderivative of sin^3(x). If F(1)=0 then F(8)=?

The answer: 0.632

How do I get to that answer? Do I find the antiderivatie and solve for F(x) when x=8?

Answer 1

Yes. Find the anti derivative and solve that answer for x = 8.

Answer 2

Alright, I found -1/4cos(x)^4 but I didn't get the right answer.
Did I dint the wrong anti-derivative? Do I have to do reverse chain rule and get... (-1/4cos(x))sin(x)^4?

Answer 3

i am still lost can someone please explain

Answer 4

my anti deriv.. i got 1/4 Cosx^4 + C

what do i do next.. = [

Answer 5

Your antiderivative is not correct.

You need a u substitution. Or if you have not learned that try NINT in the calculator.

For the u substitution, let u = cos x and du=-sinx . (this is after you changed the integral to sin^3x = sin^2x *sinx =(1-cos^2x)(-sinx). Don't forget the - sign in front of the integral too. Then do the u sub