How do I find an expression for f(x), with the properties, f'(x)=sin(x)/x and f(1)=1?

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Answer 1 · 2018-04-21T18:44:23

#intsinx/xdx=Si(x)+0.946083#

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#f'(x)=sinx/x#

#f(1)=1#

To find #f(x)# we need to take the integral of #f'(x)#:

#intsinx/xdx=Si(x)+C#

This is a special integral and is called the Sinc function in signal processing.

#int_0^1sinx/xdx=Si(1)=0.946083#

#intsinx/xdx=Si(x)+0.946083#

The constant #C# is calculated through numerical integration.