Integrating a function

In summary, the conversation revolved around two equations that needed to be solved with integration and limits from 0 to 2pi. The expert advised showing effort before receiving help and suggested using the properties of Sin(t) and Cos(t) terms. The OP then mentioned getting "0" for both results and the expert asked for the attempted solution. The OP corrected their mistake and confirmed getting "0" as the result for both equations.
  • #1
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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
 
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  • #2
What have you tried? You need to make a reasonable effort before we can provide any help.
 
  • #3
blackbear said:
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?
 
  • #4
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.
 
Last edited:
  • #5
I computed both the integration and getting "0" for both results!
 
  • #6
blackbear said:
I computed both the integration and getting "0" for both results!

Probably related to integrating sinusoidal functions from 0 to 2*PI, eh?
 
  • #7
yes...the integrating result with 0 to pi gave me the "zero" results.
 
  • #8
You really should post your attempted solution so that we can see what's plaguing you...
 
  • #9
blackbear said:
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.
 
  • #10
my mistake..my result came to be "0" for both the equations when the limits are from 0 to 2pi.

regards
 

What is integration?

Integration is a mathematical process of finding the area under a curve or the accumulation of a quantity over a given interval.

What is the difference between integration and differentiation?

Integration and differentiation are inverse operations. While integration finds the area under a curve, differentiation finds the slope of a curve at a given point.

What is the fundamental theorem of calculus?

The fundamental theorem of calculus states that integration and differentiation are inverse operations. This means that integration can be used to find the original function when given its derivative, and vice versa.

What are the different methods of integration?

The different methods of integration include substitution, integration by parts, partial fractions, trigonometric substitution, and numerical integration.

How is integration used in real life?

Integration has many real-life applications, such as calculating the area under a curve to find the volume of a 3D object, determining the distance traveled by an object with varying velocity, and finding the average value of a function over a given interval.

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