[SOLVED] Definite Intgral Involving lnx

Mar 2010
15
0
This is the equation:

\(\displaystyle \frac{d}{dx} \int_{-1}^{lnx^2} (4tsint)^\frac{1}{3} dt \)

and this is what I have:

\(\displaystyle (4xsinx)^\frac{1}{3} \Bigg|_{-1}^{lnx^2}\)

Now where do I go from here?
 
Apr 2010
384
153
Canada
This is the equation:

\(\displaystyle \frac{d}{dx} \int_{-1}^{lnx^2} (4tsint)^\frac{1}{3} dt \)

and this is what I have:

\(\displaystyle (4xsinx)^\frac{1}{3} \Bigg|_{-1}^{lnx^2}\)

Now where do I go from here?
This follows from the fundemental theorem of calculus and what have there is not correct.

\(\displaystyle \frac{d}{dx} \int_{a}^{g(x)} f(t)dt = f[g(x)]g`(x) \)

Can you compute knowing the above?
 
Mar 2010
15
0
This follows from the fundemental theorem of calculus and what have there is not correct.

\(\displaystyle \frac{d}{dx} \int_{a}^{g(x)} f(t)dt = f[g(x)]g`(x) \)

Can you compute knowing the above?
Is this what I should have?

\(\displaystyle (4lnx^2sinlnx^2)^\frac{1}{3} \frac{2x}{x^2} \Bigg|_{-1}^{lnx^2} \)
 
Apr 2010
384
153
Canada
Is this what I should have?

\(\displaystyle (4lnx^2sinlnx^2)^\frac{1}{3} \frac{2x}{x^2} \Bigg|_{-1}^{lnx^2} \)
From above,

\(\displaystyle \frac{d}{dx} \int_{-1}^{lnx^2} (4tsint)^\frac{1}{3} dt = [4(lnx^2)sin(lnx^2)]^\frac{1}{3} * \frac{2}{x} \)

We do not evaluate here which is what you have in your post. We are finished, this is the answer!
 
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Mar 2010
15
0
From above,

\(\displaystyle \frac{d}{dx} \int_{-1}^{lnx^2} (4tsint)^\frac{1}{3} dt = [4(lnx^2)sin(lnx^2)]^\frac{1}{3} * \frac{2}{x} \)

We do not evaluate here which is what you have in your post. We are finished, this is the answer!

0o0h!!! Thank you s0o0 much!!! (Yes)