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2*sqrt(x)

Integral of 2*sqrt(x) dx

Limits of integration:

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The graph:

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Piecewise:

The solution

You have entered [src]
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012xdx\int\limits_{0}^{1} 2 \sqrt{x}\, dx
Integral(2*sqrt(x), (x, 0, 1))
Detail solution
  1. The integral of a constant times a function is the constant times the integral of the function:

    2xdx=2xdx\int 2 \sqrt{x}\, dx = 2 \int \sqrt{x}\, dx

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

      xdx=2x323\int \sqrt{x}\, dx = \frac{2 x^{\frac{3}{2}}}{3}

    So, the result is: 4x323\frac{4 x^{\frac{3}{2}}}{3}

  2. Add the constant of integration:

    4x323+constant\frac{4 x^{\frac{3}{2}}}{3}+ \mathrm{constant}


The answer is:

4x323+constant\frac{4 x^{\frac{3}{2}}}{3}+ \mathrm{constant}

The answer (Indefinite) [src]
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4x323{{4\,x^{{{3}\over{2}}}}\over{3}}
The graph
0.001.000.100.200.300.400.500.600.700.800.9004
The answer [src]
4/3
43{{4}\over{3}}
=
=
4/3
43\frac{4}{3}
Numerical answer [src]
1.33333333333333
1.33333333333333
The graph
Integral of 2*sqrt(x) dx

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