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Homework Statement
[tex]$g(x)=\int _{2 }^{\sin x}\sqrt{1- t^2}dt$[/tex]
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).Homework Statement
[tex]g(x)=\int _{2 }^{\sin x}\sqrt{1- t^2}dt[/tex]
whats g'(x)...
Homework Equations
The Attempt at a Solution
how to find the antiderivative of sqrt(1-t^2)?
how to find the antiderivative of sqrt(1-t^2)?
Just to add to what Mark44 says …Use the Fundamental Theorem of Calculus to find g'(x) …
Homework Statement
[tex]g(x)=\int _{2 }^{\sin x}\sqrt{1- t^2}dt[/tex]
whats g'(x)...
Homework Equations
The Attempt at a Solution
how to find the antiderivative of sqrt(1-t^2)?
The problem does not ask you to find the anti-derivative nor is it necessary.Try t=sin(u) or t=cos(u)
okay, that make sense but what if i have a function like this: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]
You can find dg/dy directly from the "Fundamental Theorem of Calculus" and then use the chain rule to find dg/dx.