integrate [x]{x}dx

√-1Human

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I need to integrate [x]{x}dx, where square bracket x is the integer part of a real number x and curly bracket x is the fractional part of x. Can you help me find an expression for [x]{x},or give the steps to integrate it? The integral is from 0 to 5, but a general method for finding the solution would help.
 
√-1Human;381826 said:
I need to integrate [x]{x}dx, where square bracket x is the integer part of a real number x and curly bracket x is the fractional part of x. Can you help me find an expression for [x]{x},or give the steps to integrate it? The integral is from 0 to 5, but a general method for finding the solution would help.
Just to be clear, are the integer parts and fractional parts being multiplied? Thank you! ;)
 
√-1Human;381826 said:
I need to integrate [x]{x}dx, where square bracket x is the integer part of a real number x and curly bracket x is the fractional part of x. Can you help me find an expression for [x]{x},or give the steps to integrate it? The integral is from 0 to 5, but a general method for finding the solution would help.
Look at the graph.

The problem is: \(\displaystyle \displaystyle\int_0^5 {\left\lfloor x \right\rfloor \cdot \left( {x - \left\lfloor x \right\rfloor } \right)dx} \)

Note that \(\displaystyle \left\{ x \right\} = \left( {x - \left\lfloor x \right\rfloor } \right)\)
 
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