Question

what is the best way to solve a double integral question without drawing the figure we need to integrate over?

Answer 1

guessing lol

Answer 2

havent tried doubles yet....

Answer 3

lol.. but you said you were guessing..

Answer 4

whats the function or functions to double integrate :)

Answer 5

yeah giv us the function..

Answer 6

and make it a hard one lol

Answer 7

something with an exponent of 3 in it ;)

Answer 8

and a negative

Answer 9

let it be a double integral of 4xy-y^3 over the area bounded by the curves y=x^2 n y=x^(1/2)

Answer 10

if we do the x we get......umm........how do we do doubles anyways?

Answer 11

is this confined to a single plane right?

Answer 12

i see the football shape made by the bounds of x^2 and sqrt(x)

Answer 13

the region bounded by those curves looks like a rugby ball..

Answer 14

dunno what to do with the 4xy-y^3 function tho..... how does that come into play?

Answer 15

if we int with respect to y it goes; 2xy^2-y^4/4 right?

Answer 16

and with respect to x its: 4yx^3/3 +xy^3 ??

Answer 17

the major problem n which also the 1st step is to find the limits for the double integral for individual x and y.. once u r able to get that.. then its more or less like normal integration..

Answer 18

how hard is it to find limits

solve sqrt(x) = x^2

Answer 19

x^4 = x
x(x^3 -1) =0

x=0, x=1 for real solutions

Answer 20

when x=0 , y= 0

when x=1, y= 1

Answer 21

so its just \[\int\limits_{0}^{1}\int\limits_{0}^{1} f(x,y) dx dy \]

Answer 22

doesnt matter which order u integrate, in the above I do x first

Answer 23

so f(x,y) = 4xy-y^3

int f dx = 2x^2 y -xy^3 [ from x=1..x=0]

= ( [2y -y^3 ] - [0] )
= 2y -y^3


now we integrate that with respect to y , from y=0 to y=1

Answer 24

so we get [ y^2 -y^4 / 4 ] from y=1..y=0

= 1- (1/4) = 3/4 //final answer