Integral from 0 to 5 24e^-6t cos(2t) dt

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In summary, the conversation is about a person needing help with an integral and finding the anti-derivative in an integral table. They are having trouble finishing the problem and are advised to use integration by parts and evaluate the solution at the end points.
  • #1
smith5753
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I need help with this integral.

w= the integral from 0 to 5

24e^-6t cos(2t) dt.

i found the the integration in the integral table.

(e^ax/a^2 + b^2) (a cos bx + b sin bx)

im having trouble finishing the problem from here.
 
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  • #2


use integration by parts.
 
  • #3


smith5753 said:
I need help with this integral.

w= the integral from 0 to 5

24e^-6t cos(2t) dt.

i found the the integration in the integral table.

(e^ax/a^2 + b^2) (a cos bx + b sin bx)

im having trouble finishing the problem from here.
What exactly are you having problems with? You have the anti-derivative, all you need to do now is evaluate it at then end points.
 

FAQ: Integral from 0 to 5 24e^-6t cos(2t) dt

1. What is the purpose of calculating the integral from 0 to 5 for the given function?

The integral from 0 to 5 for the given function is used to find the total area under the curve of the function within the interval of 0 to 5. This can be used to solve various physics and engineering problems, such as calculating displacement, velocity, and acceleration.

2. How do you solve the given integral?

To solve the given integral, we can use integration by parts or trigonometric substitution, depending on the complexity of the function. First, we integrate the function, then evaluate it at the upper and lower limits of the given interval, and finally subtract the lower value from the upper value to find the total area.

3. What is the importance of the constant 24e^-6t in the given function?

The constant 24e^-6t in the given function represents the rate of change of the function with respect to time. This is often used in physics to model exponential decay or growth processes, such as radioactive decay or population growth.

4. Can the given integral be solved using a calculator or software?

Yes, the given integral can be solved using a calculator or software, such as Wolfram Alpha or Mathematica. However, it is important to understand the steps and concepts behind the solution, rather than relying solely on technology.

5. What is the significance of the cosine function in the given integral?

The cosine function in the given integral represents the periodic nature of the function. This is often used in physics to model oscillating systems, such as a pendulum or a spring. The cosine function can also be used to find the amplitude, frequency, and phase shift of the oscillations.

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