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

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

Limits of integration:

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The solution

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∫21(4x3−2x) dx\int\limits_{2}^{1} \left(4 x^{3} - 2 x\right)\, dx 
Integral(4*x^3 - 2*x, (x, 2, 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:

      ∫(−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: x4−x2x^{4} - x^{2}

  2. Add the constant of integration:

    x4−x2+constantx^{4} - x^{2}+ \mathrm{constant}

The answer is:

x4−x2+constantx^{4} - x^{2}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                             
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∫(4x3−2x) dx=C+x4−x2\int \left(4 x^{3} - 2 x\right)\, dx = C + x^{4} - x^{2}
Simplify
The graph
1.002.001.101.201.301.401.501.601.701.801.90050
Plot the graph f(x)
The answer [src] 
-12
−12-12 
=
= 
-12
−12-12 
-12
Numerical answer [src] 
-12.0
-12.0

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

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