evaluate the following repeated integral
int(0-pi/2) ( int(y-pi/1) cosysinxdxdy)
i have never seen a question like this please help
To start with, evaluate the inner integral...
$\displaystyle \displaystyle \int_y^{\frac{\pi}{2}}{\cos{y}\sin{x}\,dx}$.
Here, since you are integrating w.r.t. $\displaystyle \displaystyle x$, any function of $\displaystyle \displaystyle y$ is treated as a constant.
ok but what do you mean by INNER integral?
i assume from what you've said you are expected to integrate wrt x then integrate the RESULT wrt y? its not the actual differentiation and integration i can't do its understanding what the question is even asking
to be honest i don't even need to solve the answer its all by the by really, i just want to know whats its asking...
Does it make more sense if it's written like this?
$\displaystyle \displaystyle \int_{0}^{\frac{\pi}{2}}{\left[\int_0^{\frac{\pi}{2}}{\cos{y}\sin{x}\,dx}\right]\,dy}$
Can you see that there is an "inner" integral, which needs to be evaluated first, and an "outer" integral?
You should review the chapter in your text that deals with multiple integration. Alternatively you can take a gander at the stickied thread at the top of this forum! http://www.mathhelpforum.com/math-he...on-146568.html
Essentially, if you have a series of integrals you have to evaluate them in the order of most functions in the bounds to least. In other words, if you have an integral of the form,
$\displaystyle \int_a^b \int_{f(x)}^{g(x)} H(x,y)dydx $
You need to evaluate the integral with the bounds dealing with the functions of x first, then evaluate the integral with the constant bounds. Doing it the other way around won't produce a numerical result.