Mister Exam

Integral of 1/5x dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src]
  1     
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 |  x   
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 |  5   
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01x5dx\int\limits_{0}^{1} \frac{x}{5}\, dx
Integral(x/5, (x, 0, 1))
Detail solution
  1. The integral of a constant times a function is the constant times the integral of the function:

    x5dx=xdx5\int \frac{x}{5}\, dx = \frac{\int x\, dx}{5}

    1. The integral of xnx^{n} is xn+1n+1\frac{x^{n + 1}}{n + 1} when n1n \neq -1:

      xdx=x22\int x\, dx = \frac{x^{2}}{2}

    So, the result is: x210\frac{x^{2}}{10}

  2. Add the constant of integration:

    x210+constant\frac{x^{2}}{10}+ \mathrm{constant}


The answer is:

x210+constant\frac{x^{2}}{10}+ \mathrm{constant}

The answer (Indefinite) [src]
  /             
 |             2
 | x          x 
 | - dx = C + --
 | 5          10
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x5dx=C+x210\int \frac{x}{5}\, dx = C + \frac{x^{2}}{10}
The graph
0.001.000.100.200.300.400.500.600.700.800.900.00.4
The answer [src]
1/10
110\frac{1}{10}
=
=
1/10
110\frac{1}{10}
1/10
Numerical answer [src]
0.1
0.1
The graph
Integral of 1/5x dx

    Use the examples entering the upper and lower limits of integration.