# Homework Help: Antiderivative of a function problem

1. Jan 8, 2010

### Slimsta

1. The problem statement, all variables and given/known data
$$g(x)=\int _{2 }^{\sin x}\sqrt{1- t^2}dt$$
whats g'(x)...

2. Relevant equations

3. The attempt at a solution
how to find the antiderivative of sqrt(1-t^2)?

2. Jan 9, 2010

### rock.freak667

Try t=sin(u) or t=cos(u)

3. Jan 9, 2010

### Staff: Mentor

I have edited your formula slightly so that it now shows g(x), not just (x). You had extra \$ characters that shouldn't have been there.
Use the Fundamental Theorem of Calculus to find g'(x). You will also need the chain rule since your integral isn't strictly a function of just x, but is a function of sin(x).

4. Jan 9, 2010

### tiny-tim

Hi Slimsta!
Just to add to what Mark44 says …

the beauty of using the Fundamental Theorem of Calculus is that you don't need to know the antiderivative.

5. Jan 9, 2010

### HallsofIvy

The problem does not ask you to find the anti-derivative nor is it necessary.
Letting y= sin(x), this is
$$g(y)=\int_2^y \sqrt{1- t^2} dt[/itex] You can find dg/dy directly from the "Fundamental Theorem of Calculus" and then use the chain rule to find dg/dx. 6. Jan 10, 2010 ### Slimsta okay, that make sense but what if i have a function like this: [tex]\int _{3\pi /4}^{\pi }(3 \sec ^2x -\frac{6 }{\pi })dx$$

this is confusing me :S

7. Jan 10, 2010

### Bohrok

That's a definite integral, so that gives you the signed area between the limits of integration, or just a number. What's the derivative of a constant?

A variable (other than x since x would be the dummy variable) in either of the limits of integration would make it a function.

8. Jan 11, 2010

### Slimsta

hh i already figured that out.. i just took out the 3 and then it becomes tanx - 2/pi x and then its easy..