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4x^3-2x^2
Solving integrals/ 4x^3-2x^2

Integral of 4x^3-2x^2 dx

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Piecewise:

The solution

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0
∫01(4x3−2x2) dx\int\limits_{0}^{1} \left(4 x^{3} - 2 x^{2}\right)\, dx 
Integral(4*x^3 - 2*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:

      ∫4x3 dx=4∫x3 dx\int 4 x^{3}\, dx = 4 \int x^{3}\, dx

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

        ∫x3 dx=x44\int x^{3}\, dx = \frac{x^{4}}{4}

      So, the result is: x4x^{4}

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

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

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

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

      So, the result is: −2x33- \frac{2 x^{3}}{3}

    The result is: x4−2x33x^{4} - \frac{2 x^{3}}{3}

  2. Now simplify:

    x3(x−23)x^{3} \left(x - \frac{2}{3}\right)

  3. Add the constant of integration:

    x3(x−23)+constantx^{3} \left(x - \frac{2}{3}\right)+ \mathrm{constant}

The answer is:

x3(x−23)+constantx^{3} \left(x - \frac{2}{3}\right)+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                                
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 | /   3      2\           4   2*x 
 | \4*x  - 2*x / dx = C + x  - ----
 |                              3  
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x4−2 x33x^4-{{2\,x^3}\over{3}}
Simplify
The graph
0.001.000.100.200.300.400.500.600.700.800.902.5-2.5
Plot the graph f(x)
The answer [src] 
1/3
13{{1}\over{3}} 
=
= 
1/3
13\frac{1}{3}
Simplify
Numerical answer [src] 
0.333333333333333
0.333333333333333
The graph
Integral of 4x^3-2x^2 dx

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

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