Question

About Multiple Integral
integral of (x^2+xy^3)dxdy R=[2,3]*[4,7]

Answer 1

X goes from 2 to 3 and
Y goes from 4 to 7?

Answer 2

\[\int\limits_{x = 2}^{3}\int\limits_{y = 4}^{7}(x^{2} + xy^{3})dxdy\]
Is this what you meant?

Answer 3

Yes! you are right.
how about the integral?

Answer 4

\[\int\limits_4^7\int\limits_2^3 (x^2+xy^3) \text dx\text dy\]

Answer 5

Well, the trick here is to just evaluate one integral at a time, and with respect to only one variable, first.

In other words, you either integrate as if y is a constant, or as if x is a constant.
It's your call
Can you do it? :)

Answer 6

make sure you take the limits in the right order ,

Answer 7

\[=\int\limits_4^7\left(\int\limits_2^3 (x^2+xy^3) \text dx\right)\text dy\]

Answer 8

treat y as a constant in the inner integral

Answer 9

=int[7,4](x^3/3+x^2y^3/2|[3,2])dy
=

Answer 10

good \[=\int\limits_4^7\left(\left.\frac{x^3}{3}+\frac{x^2y^3}{2}\right|_2^3\right)dy\]
now take the inner limits for x,