Integration of multiple exponentials

In summary, the person is struggling with solving an integral involving exponential functions. They have attempted to use substitution and move the constant outside of the integral, but are unsure of how to proceed. They are seeking help with solving the problem.
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Mzzed
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Homework Statement


I am struggling with solving this integral that seems to look easy on the surface but integration isn't my strong suit and so I'm not 100% sure on how to go about solving this:

∫ (120(e-15.24t - e-39984.75t))2dt

where the integration is from 0 to 0.3

Homework Equations

The Attempt at a Solution


I have tried using substitution for everything within the squared brackets and moved the 1202 outside of the integral. However this only seemed to make the question longer but that may simply be because I am not familiar with some techniques that I may have forgotten. This is not a homework question so any answers would be helpful.
 
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  • #2
Mzzed said:

Homework Statement


I am struggling with solving this integral that seems to look easy on the surface but integration isn't my strong suit and so I'm not 100% sure on how to go about solving this:

∫ (120(e-15.24t - e-39984.75t))2dt

where the integration is from 0 to 0.3

Homework Equations

The Attempt at a Solution


I have tried using substitution for everything within the squared brackets and moved the 1202 outside of the integral. However this only seemed to make the question longer but that may simply be because I am not familiar with some techniques that I may have forgotten. This is not a homework question so any answers would be helpful.
Moving out 1202 is a good step, but substitution does not make the integration easier. Expand (e-15.24t - e-39984.75t)2, you get three exponents, easy to integrate.
 
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Gahh see I always overlook the simple things hahah thankyou
 

FAQ: Integration of multiple exponentials

What does "integration of multiple exponentials" mean?

The integration of multiple exponentials refers to the process of finding the antiderivative or integral of a function that contains multiple exponential terms. This involves using mathematical techniques to solve for a general solution that satisfies the given function.

Why is the integration of multiple exponentials important?

The integration of multiple exponentials is important because it allows us to solve complex mathematical problems and model real-world phenomena. Many physical and natural processes can be described using exponential functions, and being able to integrate them helps us understand and predict their behavior.

What are the main techniques used for integrating multiple exponentials?

The main techniques for integrating multiple exponentials include substitution, integration by parts, and partial fractions. These techniques can be used alone or in combination to simplify the integral and arrive at a solution.

Are there any special cases or rules for integrating multiple exponentials?

Yes, there are some special cases and rules for integrating multiple exponentials. For example, if the exponentials have the same base, we can use the properties of exponents to combine them and simplify the integral. Additionally, there are specific techniques for integrating certain types of exponential functions, such as trigonometric and hyperbolic exponentials.

What are some real-world applications of integrating multiple exponentials?

The integration of multiple exponentials has many real-world applications, including in physics, chemistry, biology, economics, and engineering. For example, it can be used to model population growth, radioactive decay, chemical reactions, and financial investments. It is also essential in solving differential equations, which are used to describe a wide range of natural phenomena.

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