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2*x-x^2
Solving integrals/ 2*x-x^2

Integral of 2*x-x^2 dx

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The solution

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∫01(−x2+2x) dx\int\limits_{0}^{1} \left(- x^{2} + 2 x\right)\, dx 
Integral(2*x - x^2, (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:

      ∫(−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}

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

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

      So, the result is: x2x^{2}

    The result is: −x33+x2- \frac{x^{3}}{3} + x^{2}

  2. Now simplify:

    x2(3−x)3\frac{x^{2} \left(3 - x\right)}{3}

  3. Add the constant of integration:

    x2(3−x)3+constant\frac{x^{2} \left(3 - x\right)}{3}+ \mathrm{constant}

The answer is:

x2(3−x)3+constant\frac{x^{2} \left(3 - x\right)}{3}+ \mathrm{constant}

The answer (Indefinite) [src] 
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∫(−x2+2x) dx=C−x33+x2\int \left(- x^{2} + 2 x\right)\, dx = C - \frac{x^{3}}{3} + x^{2}
Simplify
The graph
0.001.000.100.200.300.400.500.600.700.800.9002
Plot the graph f(x)
The answer [src] 
2/3
23\frac{2}{3} 
=
= 
2/3
23\frac{2}{3} 
2/3
Numerical answer [src] 
0.666666666666667
0.666666666666667
The graph
Integral of 2*x-x^2 dx

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

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