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x^(1/2)-x^2
Solving integrals/ x^(1/2)-x^2

Integral of x^(1/2)-x^2 dx

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The solution

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∫01(x−x2) dx\int\limits_{0}^{1} \left(\sqrt{x} - x^{2}\right)\, dx 
Integral(sqrt(x) - x^2, (x, 0, 1))
Detail solution

  1. Integrate term-by-term:

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

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

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

      ∫(−x2) dx=−∫x2 dx\int \left(- x^{2}\right)\, dx = - \int x^{2}\, dx

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

        ∫x2 dx=x33\int x^{2}\, dx = \frac{x^{3}}{3}

      So, the result is: −x33- \frac{x^{3}}{3}

    The result is: 2x323−x33\frac{2 x^{\frac{3}{2}}}{3} - \frac{x^{3}}{3}

  2. Add the constant of integration:

    2x323−x33+constant\frac{2 x^{\frac{3}{2}}}{3} - \frac{x^{3}}{3}+ \mathrm{constant}

The answer is:

2x323−x33+constant\frac{2 x^{\frac{3}{2}}}{3} - \frac{x^{3}}{3}+ \mathrm{constant}

The answer (Indefinite) [src] 
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∫(x−x2) dx=C+2x323−x33\int \left(\sqrt{x} - x^{2}\right)\, dx = C + \frac{2 x^{\frac{3}{2}}}{3} - \frac{x^{3}}{3}
Simplify
The graph
0.001.000.100.200.300.400.500.600.700.800.900.00.5
Plot the graph f(x)
The answer [src] 
1/3
13\frac{1}{3} 
=
= 
1/3
13\frac{1}{3}
Упростить
Numerical answer [src] 
0.333333333333333
0.333333333333333
The graph
Integral of x^(1/2)-x^2 dx

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

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