Can you integrate 0.5etm/s2 in terms of e?

Thread starter rlwhiting1
Start date Jan 13, 2011
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Integrate

In summary, "e" is a mathematical constant with a value of approximately 2.71828 that is used in integration as the base of the natural logarithm. It is important in integration because it simplifies many integrals and has applications in various fields. It is related to the area under a curve through the natural logarithm and can be used in indefinite integration by factoring it out of the integral.

Jan 13, 2011

rlwhiting1

Homework Statement

a_t= 0.5e^tm/s²

Homework Equations

a_t = dv/dt

The Attempt at a Solution

v = integration of 0.5e^t

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Jan 13, 2011

Char. Limit

Gold Member

So what is the integral of e^(t) dt?

Jan 13, 2011

HallsofIvy

Science Advisor

Homework Helper

If you know that the derivative of [itex]e^t[/itex] is just [itex]e^t[/itex] itself, then its integral is easy.

What is "e" in integration?

"e" is a mathematical constant with a value of approximately 2.71828. It is often referred to as the "base of the natural logarithm" and is used in many mathematical functions, including integration.

How is "e" used in integration?

"e" is used in integration as the base of the natural logarithm, which is a crucial part of finding the antiderivative or integral of a function. It is also used in many integration techniques, such as integration by substitution and integration by parts.

Why is "e" important in integration?

"e" is important in integration because it allows for the simplification of many integrals and makes the process more efficient. It also has important applications in many fields, including physics, engineering, and finance.

How is "e" related to the area under a curve?

"e" is related to the area under a curve through the natural logarithm, which is used to find the antiderivative of a function. The area under a curve can be represented by the integral of that function, which often involves "e" as the base of the natural logarithm.

Can "e" be used in indefinite integration?

Yes, "e" can be used in indefinite integration, as it is a constant that can be factored out of the integral. It is often used in conjunction with other integration techniques to find the antiderivative of a function.