Antiderivative of a function problem

[Slimsta]

Homework Statement

$$g(x)=\int _{2 }^{\sin x}\sqrt{1- t^2}dt$$
whats g'(x)...

Homework Equations

The Attempt at a Solution

how to find the antiderivative of sqrt(1-t^2)?

 

[rock.freak667]

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

 

[Mark44]

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.

Homework Statement

$$g(x)=\int _{2 }^{\sin x}\sqrt{1- t^2}dt$$
whats g'(x)...

Homework Equations

The Attempt at a Solution

how to find the antiderivative of sqrt(1-t^2)?

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).

 

[tiny-tim]

Hi Slimsta!

how to find the antiderivative of sqrt(1-t^2)?

Use the Fundamental Theorem of Calculus to find g'(x) …

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.

 

[HallsofIvy]

Homework Statement

$$g(x)=\int _{2 }^{\sin x}\sqrt{1- t^2}dt$$
whats g'(x)...

Homework Equations

The Attempt at a Solution

how to find the antiderivative of sqrt(1-t^2)?

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

The problem does not ask you to find the anti-derivative nor is it necessary.
Letting y= sin(x), this is
[tex]g(y)=\int_2^y \sqrt{1- t^2} dt[/itex]<br /> You can find dg/dy directly from the "Fundamental Theorem of Calculus" and then use the chain rule to find dg/dx.[/tex]

 

[Slimsta]

The problem does not ask you to find the anti-derivative nor is it necessary.
Letting y= sin(x), this is
[tex]g(y)=\int_2^y \sqrt{1- t^2} dt[/itex]<br /> You can find dg/dy directly from the "Fundamental Theorem of Calculus" and then use the chain rule to find dg/dx.[/tex]

[tex] <br /> okay, that make sense but what if i have a function like this:<br /> $$\int _{3\pi /4}^{\pi }(3 \sec ^2x -\frac{6 }{\pi })dx$$<br /> <br /> this is confusing me :S[/tex]

 

[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.

 

[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..