Question

Evaluate ∫(0,2)∫(x,2) (xsqt(1+y^3)) dy dx... Its supposed to be easier by changing the order but i dont know how

Answer 1

\[\Large \int\limits_{x=0}^2\quad\int\limits_{y=x}^2\;x\sqrt{1+y^3}\;dy\;dx\]So let's start by drawing the region we're integrating over in x and y:

Answer 2

Understand how I drew the region?

Answer 3

yes, i do

Answer 4

So to reverse them we would ummm..

Answer 5

and in the x direction instead of x varying between constants,

Answer 6

I can't think of the right words to explain this.. grrr.
Hopefully the pictures help a little bit :c

Answer 7

\[\Large \int\limits\limits_{x=0}^2\quad\int\limits\limits_{y=x}^2\;x\sqrt{1+y^3}\;dy\;dx\qquad\to\qquad\int\limits\limits_{y=0}^2\quad\int\limits\limits_{x=0}^y\;x\sqrt{1+y^3}\;dx\;dy\]

Answer 8

Oh, Okay. I understand what you did. The second graph was basically a rectangle to see where it starts and ends. Thank You!!!

Answer 9

yay \c:/