- #1

- 192

- 1

Suppose we're asked to find the derivative of the integral

[tex]f(x)~=~\int_{-13}^{sin~x} \sqrt{1+t^2}~dt[/tex]

Now, the solution apparently looks like this:

[tex]f(x)^{\prime} = \sqrt{1+sin^2(x)}\cdot~cos(x)[/tex]

Why?

Why does the solution contain the upper limit `plugged in` ?

A more sensible answer (to me) would be [tex]\sqrt{1+x^2}[/tex]