Question

Evaluate the iterated integral.
2 2
∫ ∫ xydydx
1 x

Explain please.

Answer 1

\[\int\limits_{1}^{2}\int\limits_{x}^{2}xy~dydx\]
Solve with respect to y, treating x as a constant
\[\huge \int\limits\limits_{1}^{2}[\frac{xy^{2}}{2}]_{x}^{2} dx\]
\[\huge \int\limits\limits\limits_{1}^{2}2x-\frac{x^3}{2}dx\]
\[[\huge x^2-\frac{x^4}{(4)2}]_{1}^{2}\]
\[\huge =\frac{9}{8}\]

Answer 2

where you don't understand just say it out :)

Answer 3

how did you know to begin solving with respect to y instead of x?

Answer 4

the 'dy' tells

Answer 5

thank you so much i understand it =P!

Answer 6

Its basically separated like this
\[\huge (\int\limits_{1}^{2}[\int\limits_{x}^{2}xydy]dx)\]

Answer 7

do the inner part first

Answer 8

for the second part when you pluged in 2 and x did you plug it into the y or the x?

Answer 9

the 'y' because of 'dy'

Answer 10

thank you i completed the problem! =]