Question

double Integral , including change of limit

Answer 1

\[\int\limits_{0}^{pi/4}\int\limits_{sinx}^{cosx}xy dydx\]

Answer 2

@experimentX can you figure it out?

Answer 3

@.Sam. helppppp

Answer 4

lol ... 0 to pi is for x??

Answer 5

yeah

Answer 6

@asnaseer

Answer 7

plz make me understand how to do these tyoe of questions

Answer 8

Hi @wasiqss
brb

Answer 9

ok ash

Answer 10

are you trying to change limits or ... just trying to solve it??

Answer 11

\[\int_{0}^{\pi/4} \int_{\sin x}^{\cos x}xy dy dx \]
The integral inside has limits (function of x) so integrate y and then put the limits

Answer 12

* with respect to y

Answer 13

i want to learn to change limits first

Answer 14

@ash i dint get it

Answer 15

I'm trying to recall, wait for some time

Answer 16

definitely ... not a good problem to learn change of limits!!

Answer 17

Change of limits is not required
\[\int_0^{\pi/4}\int_{\sin x}^{\cos x} xy dy dx\]
We'll evaluate the inner integral, treating x as constant
\[\int_0^{\pi/4}x(\int_{\sin x}^{\cos x} y dy) dx\]
\[\int_0^{\pi/4}x([\frac{y^2}2]_{\sin x}^{\cos x}) dx\]
\[\int_0^{\pi/4}x(\frac{\cos^2 x-\sin^2 x }{2}) dx\]
\[\int_0^{\pi/4}x(\frac{\cos 2x}{2}) dx\]
I think you can solve the rest, Can't you?

Answer 18

@lalaly you are too late lol :P

Answer 19

@ash2326 thanks :)

Answer 20

@lalaly fail xD

Answer 21

lol sorry wass i was feeding lena lemons:P

Answer 22

lol , lemons, arghhhhh they are sour :P

Answer 23

dint she cry or pull your hears while you were doing it :p

Answer 24

Shes Loves it !!

Answer 25

substitution and change of limits
http://ocw.mit.edu/courses/mathematics/18-02sc-multivariable-calculus-fall-2010/part-a-double-integrals/session-53-change-of-variables/
i found this part the most difficult in multivariable calculus

Answer 26

i hated the graphs lol

Answer 27

\[\int\limits_{1}^{5}\int\limits_{0}^{x^2}(1+2x)e^(x+y)dydx\]

Answer 28

@ash2326 how to do this

Answer 29

x + y is exponent of e right?

Answer 30

seriously ... are you trying to evaluate this or trying to evaluate using substitution??

Answer 31

yes lgb

Answer 32

1 + 2x is constant so pull out...then let u = x+ y should be visible from there

Answer 33

lol experiment, basically , my aim is to evaulaute using change of limits

Answer 34

no change of limits here either...dx would be hard though

Answer 35

fine then , cause i dont need to know how to integrate, only how to interchange the limits

Answer 36

oh wait no...dx is straightforward to...it's just u-subs

Answer 37

@experimentX thanks for vidz

Answer 38

yw

Answer 39

i need to see it myself over again and again ... lol

Answer 40

can you find an integral where the constant limits are in the inside...those do interchange of limits