Question

The double integral ∫ from 0 to 1 ∫ from x to 1 cos(y^2) dydx ? I have tried doing dx then dy but end up with the same problem of having cos(y^2). Any ideas on what I need to do?

Answer 1

u substitution i guess.. did u just try it...?

Answer 2

\[\int\limits_{0}^{1} \cos(y^2)\]

Answer 3

did i write it correctly?

Answer 4

Yes

Answer 5

\[\large \int \limits_0^1 \int \limits_0^x \cos(y^2) ~dy dx\]

Answer 6

its a double integral, right ?

Answer 7

sorry i think @ganeshie8 is right.. i forgot that it is double integration....

Answer 8

oops jnx ganes the x and 0 need to switch

Answer 9

and it needs to be a one, hold on I need to write it. I was trying to do substitution and am getting confused.

Answer 10

\[\large \int \limits_0^1 \int \limits_x^1 \cos(y^2) ~dy dx\]

like this ?

Answer 11

\[\int\limits_{0}^{1} \int\limits_{x}^{1} \cos(y ^{2}) dydx\]

Answer 12

yes

Answer 13

Substitution tricks will not work

Answer 14

try to work \(\large dxdy\) instead

Answer 15

change the order of integration ^

Answer 16

I did but you end up with the same problem

Answer 17

It was the first thing I tried

Answer 18

\[\large \int \limits_0^1 \int \limits_x^1 \cos(y^2) ~dy dx = \large \int \limits_{\cdots}^{\cdots} \int \limits_{\cdots}^{\cdots} \cos(y^2) ~\color{red}{dxdy}\]

Answer 19

\[\int\limits_{x}^{1} cosy ^{2} dx\]

Answer 20

\[\large \int \limits_0^1 \int \limits_x^1 \cos(y^2) ~dy dx = \large \int \limits_0^1 \int \limits_0^y \cos(y^2) ~\color{red}{dxdy}\]

Answer 21

Notice that cos(y^2) is just a constant when you work dx - so you can push it out of integral

Answer 22

\[\large \int \limits_0^1 \int \limits_x^1 \cos(y^2) ~dy dx = \large \int \limits_0^1 \int \limits_0^y \cos(y^2) ~\color{red}{dxdy}\]

\[\large = \large \int \limits_0^1 \cos(y^2) \int \limits_0^y ~\color{red}{dxdy}\]

Answer 23

but when you substitute 1 and zero in are you not left with cosy^2? or do you not switch the \[\int\limits_{.}^{.}\]

Answer 24

bounds also change when you change the order of integration

Answer 25

Ok so I need to find the new bounds?

Answer 26

Exactly ! but i changed the bounds already, see if that looks okay above ^

Answer 27

Looks good, thank you for the help!

Answer 28

np :) evaluating it should be trivial... good luck !