Question

double integral

Answer 1

\[x^{3}y \] for R bounded by y = x^2 and y = 2x please help

Answer 2

@missylulu

Answer 3

firstly trace these two curves and find the point of intersection and check the variation for x and y

Answer 4

x = 0, 2!

Answer 5

ya x=0,2 and corresponding to that y=0,4
so the two points are (0,0) and (2,4) right?

Answer 6

you draw the graph...........trace these two curves...

Answer 7

you dont use y=0,4
you need to integrate from x^2 to 2x
or vice versa

you need to integrate the y first because y is dependant on x

Answer 8

i agree that you should start by drawing a graph to determine the order in which you integrate the boundaries

Answer 9

do you see which one is lower? like are the limits bottom to top?? fr om the graph

Answer 10

\[\int\limits_{0}^{2}\int\limits_{2x}^{x^2} {x^3y} dy dx\]

Answer 11

oops i wrote the integral incorrectly

Answer 12

x is from 0 to 2
so we only look at that section when considering whether x^2 or 2x should be on top of the integral

sorry my termnology may be horrible and i hope you can somewhat understand what im saying

anyways when you actually draw the graph, the area that you are integrating is between 2x and x^2

2x being on top

Answer 13

ok ok! so like for integrals where it gives you some equation you just graph it to see what to integrate it by? you dont have to create new limits or something?

Answer 14

like that interchanging limits or something lol sorry

Answer 15

well, this problem is 3 dimensional z=x^3y
but when determining the order for integrating dependant limits
just graph the boundaries to determine order in which you're integrating

Answer 16

on a side note,
using your problem as an example, if you were integrating from 0,4
or any other number greater than 2

you would have to break it up into 2 integrals

because past x=2, x^2 would be above 2x
so basically integrating from 0 to 2, then 2 to 4

Answer 17

ohhh okok! btw youre not a completeidiot i am LOL THANK YOU ^^

Answer 18

which is why drawing a graph is highly suggested, unless you can picture it in your head
but even then you're bound to screw up from time to time

Answer 19

no problem