Question

Can anyone help me with integrating this double integral calc problem

Answer 1

@amistre64 @iambatman

Answer 2

whats your first thought that comes to mind

Answer 3

this could help
\[\int\limits_{0}^{2} \int\limits_{y=0}^{y=2x}\]

Answer 4

for dy part treat 1/x^2+1 as a constant

Answer 5

yes i was hoping the asker could come to that idea ... instead of simply being told to do it

Answer 6

sorry iwas just trying to give him a hint :)

Answer 7

i know :) but hinting afterwards tends to force them to consider the options available to them in my eyes.

Answer 8

ok point noted :)

Answer 9

now @Ventricate can u do it?

Answer 10

give it a try we'll help you :)

Answer 11

what we have now is
\[\int\limits_{0}^{2} [ \int\limits_{y=0}^{y=2x}\frac{ 1 }{ x^2+1 }dy]dx=\int\limits_{0}^{2}\frac{ 1 }{ x^2+1 }[\int\limits_{y-0}^{y=2x}dy]dx\]

Answer 12

ok ??

Answer 13

oh sorryyyy guys I was in class. Yeah it's not the integrals I'm having issue with 1/u I'm not sure how to do it @sidsiddhartha @amistre64

Answer 14

should I use u sub for this?

Answer 15

no u sub needed that i would see

Answer 16

yes u can use it but look it is of the form \[\int\limits_{}^{}\frac{ dx }{ x }\]

Answer 17

its simply a matter of recognizing that you work the integral from the inside out; work the dy first since its the inner most variable and what ever is not a y, is held constant

Answer 18

oh so switch to do dx first?

Answer 19

first evaluate the dy part

Answer 20

\[\int\limits_{0}^{2}\frac{ 1 }{ 1+x^2 }.2xdx\]

Answer 21

right?

Answer 22

ooooh yes! i was doing 2x on the denominator all this time thank you!

Answer 23

yw!! :)