I'm having problems finding the partial derivatives in terms of x and y of
$\displaystyle f(x,y)=\int_{y}^{x}\cos(t^{2}) dt$
For some reason I just can't get past the cos(t^2) part and could use some help.
Thanks in advance.
I'm having problems finding the partial derivatives in terms of x and y of
$\displaystyle f(x,y)=\int_{y}^{x}\cos(t^{2}) dt$
For some reason I just can't get past the cos(t^2) part and could use some help.
Thanks in advance.
remember something called the second fundamental theorem of calculus?
it says: $\displaystyle \frac d{dx} \int_c^x f(t)~dt = f(x)$
where $\displaystyle c$ is a constant.
now it's time for a hint: when finding the partial derivative with respect to x, we treat all other variables as constants. a similar holds true for taking the partial derivative with respect to y. i don't suppose i have to tell you this, but i will anyway, $\displaystyle \int_a^b f(x)~dx = - \int_b^a f(x)~dx$