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\int_{1}^{4}\left \{ x-0.4 \right \}dxequals ({x} is a fractional part of x)

  • Option 1)

    1.3

  • Option 2)

    6.3

  • Option 3)

    1.5

  • Option 4)

    7.5

 

Answers (1)

As we learnt

Properties of Definite Integration -

For periodic function

Let Period (T) then

\int_{0}^{nT}f(n)dx= n\int_{0}^{T}f(x)dx

 

- wherein

Where f(x) is periodic function with period T and n is any integer.

 

 

Put x – 0.4 = t Þ \int_{0.6}^{3.6}\left \{ t \right \}dt=\int_{0.6}^{0.6+3}\left \{ t \right \}dt= 3\int_{0}^{1}\left ( t-\left [ t \right ] \right )dt

            = 3\left ( \frac{t^{2}}2{} \right )_{0}^{1}=\frac{3}{2}=1.5.


Option 1)

1.3

Option 2)

6.3

Option 3)

1.5

Option 4)

7.5

Posted by

Vakul

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