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Solving integrals/ 3*x^2-2*x

Integral of 3*x^2-2*x dx

Limits of integration:

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The graph:

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Piecewise:

The solution

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∫14(3x2−2x) dx\int\limits_{1}^{4} \left(3 x^{2} - 2 x\right)\, dx 
Integral(3*x^2 - 2*x, (x, 1, 4))
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:

      ∫3x2 dx=3∫x2 dx\int 3 x^{2}\, dx = 3 \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: x3x^{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 \left(- 2 x\right)\, 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: −x2- x^{2}

    The result is: x3−x2x^{3} - x^{2}

  2. Now simplify:

    x2(x−1)x^{2} \left(x - 1\right)

  3. Add the constant of integration:

    x2(x−1)+constantx^{2} \left(x - 1\right)+ \mathrm{constant}

The answer is:

x2(x−1)+constantx^{2} \left(x - 1\right)+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                             
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∫(3x2−2x) dx=C+x3−x2\int \left(3 x^{2} - 2 x\right)\, dx = C + x^{3} - x^{2}
Simplify
The graph
1.004.001.251.501.752.002.252.502.753.003.253.503.75050
Plot the graph f(x)
The answer [src] 
48
4848 
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48
4848 
48
Numerical answer [src] 
48.0
48.0

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

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