Can these two equations be solved for T with limits from 0 to 2pi?

[blackbear]

Can someone help solve these two equations:

1. T[Cos(t)] = ∫[Sin(t-x)Cos(t)]dx the limits are from 0 to 2pi

2. T[Sin(t)]=∫[Sin(t-x)Sin(t)]dx; the limits are from 0 to 2pi


Thanks

 

[Mark44]

What have you tried? You need to make a reasonable effort before we can provide any help.

 

[berkeman]

Can someone help solve these two equations:

1. T[Cos(t)] = ∫[Sin(t-x)Cos(t)]dx the limits are from 0 to 2pi

2. T[Sin(t)]=∫[Sin(t-x)Sin(t)]dx; the limits are from 0 to 2pi


Thanks

Per the PF rules, you need to show some effort at solving these problems before we can help you. But I'll offer a hint: If the integration is with respect to x (as indicated by the dx in each equation), then what can you do with the Sin(t) and Cos(t) terms in each equation?

 

[blackbear]

Well Sin(t) and Cos(t) is a constant; each of these terms will come outside the integration, if we x is the integrating variable.

 

[blackbear]

I computed both the integration and getting "0" for both results!

 

[berkeman]

I computed both the integration and getting "0" for both results!

Probably related to integrating sinusoidal functions from 0 to 2*PI, eh?

 

[blackbear]

yes...the integrating result with 0 to pi gave me the "zero" results.

 

[sEsposito]

You really should post your attempted solution so that we can see what's plaguing you...

 

[berkeman]

yes...the integrating result with 0 to pi gave me the "zero" results.

No, you said 0 to 2*PI in your original post (OP) above.

 

[blackbear]

my mistake..my result came to be "0" for both the equations when the limits are from 0 to 2pi.

regards