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Solving integrals/ x½

Integral of x½ dx

Limits of integration:

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v

The graph:

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Piecewise:

The solution

You have entered [src] 
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 |  x*1/2 dx
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0
∫01x12 dx\int\limits_{0}^{1} x \frac{1}{2}\, dx 
Integral(x*(1/2), (x, 0, 1))
Detail solution

  1. The integral of a constant times a function is the constant times the integral of the function:

    ∫x12 dx=∫x dx2\int x \frac{1}{2}\, dx = \frac{\int x\, dx}{2}

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

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

    So, the result is: x24\frac{x^{2}}{4}

  2. Add the constant of integration:

    x24+constant\frac{x^{2}}{4}+ \mathrm{constant}

The answer is:

x24+constant\frac{x^{2}}{4}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                2
 |                x 
 | x*1/2 dx = C + --
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x24{{x^2}\over{4}}
Simplify
The graph
0.001.000.100.200.300.400.500.600.700.800.900.01.0
Plot the graph f(x)
The answer [src] 
1/4
14{{1}\over{4}} 
=
= 
1/4
14\frac{1}{4}
Simplify
Numerical answer [src] 
0.25
0.25
The graph
Integral of x½ dx

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

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