Fundamental Theorem of Calculus to find Derivative

[jeeves_17]

Use the Fundamental Theorem of Calculus to find the derivative of the function



g(x) = \sqrt{x}\int sinx Ln(t) \frac{cos(t)}{t} dt



g'(x) = lnx cosx / x. By integrating this function, you receive the function g(x). Then by differentiating g(x) you receive g'(x) which is what is given, according to FTCI.


I was told I got this completely wrong. (out of 5) So looking for some help. Thanks in advance.

 

[Дьявол]

I do not understand something. Could you possibly rewrite the original problem?
Is it:

g(x)=\sqrt{x}\int{sin(x)dx} *\int{\frac{ln(t)*cos(t)}{t}dt}


Regards.

 

[jgens]

As stated, the function g(x) doesn't look quite right. Is it supposed to be defined such that,

g(x) = \sqrt x sin(x) \int_{a}^x \frac{ln(t)cos(t)}{t} \, dt

If so, then use the product rule of differentiation because g(x) can be defined in terms of the product of two functions u and v where,

u = \sqrt x sin(x)

v = \int_{a}^x \frac{ln(t)cos(t)}{t} \, dt