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Solving integrals/ x-sqrt(x)

Integral of x-sqrt(x) dx

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Piecewise:

The solution

You have entered [src] 
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∫01(−x+x) dx\int\limits_{0}^{1} \left(- \sqrt{x} + x\right)\, dx 
Integral(x - sqrt(x), (x, 0, 1))
Detail solution

  1. Integrate term-by-term:

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

      ∫(−x) dx=−∫x dx\int \left(- \sqrt{x}\right)\, dx = - \int \sqrt{x}\, dx

      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}

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

    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}

    The result is: −2x323+x22- \frac{2 x^{\frac{3}{2}}}{3} + \frac{x^{2}}{2}

  2. Add the constant of integration:

    −2x323+x22+constant- \frac{2 x^{\frac{3}{2}}}{3} + \frac{x^{2}}{2}+ \mathrm{constant}

The answer is:

−2x323+x22+constant- \frac{2 x^{\frac{3}{2}}}{3} + \frac{x^{2}}{2}+ \mathrm{constant}

The answer (Indefinite) [src] 
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∫(−x+x) dx=C−2x323+x22\int \left(- \sqrt{x} + x\right)\, dx = C - \frac{2 x^{\frac{3}{2}}}{3} + \frac{x^{2}}{2}
Simplify
The graph
0.001.000.100.200.300.400.500.600.700.800.90-0.500.25
Plot the graph f(x)
The answer [src] 
-1/6
−16- \frac{1}{6} 
=
= 
-1/6
−16- \frac{1}{6} 
-1/6
Numerical answer [src] 
-0.166666666666667
-0.166666666666667

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

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