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

Integral of x^4-x^2 dx

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The solution

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∫01(x4−x2) dx\int\limits_{0}^{1} \left(x^{4} - x^{2}\right)\, dx 
Integral(x^4 - x^2, (x, 0, 1))
Detail solution

  1. Integrate term-by-term:

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

      ∫x4 dx=x55\int x^{4}\, dx = \frac{x^{5}}{5}

    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}

    The result is: x55−x33\frac{x^{5}}{5} - \frac{x^{3}}{3}

  2. Add the constant of integration:

    x55−x33+constant\frac{x^{5}}{5} - \frac{x^{3}}{3}+ \mathrm{constant}

The answer is:

x55−x33+constant\frac{x^{5}}{5} - \frac{x^{3}}{3}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                          
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 | / 4    2\          x    x 
 | \x  - x / dx = C - -- + --
 |                    3    5 
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∫(x4−x2) dx=C+x55−x33\int \left(x^{4} - x^{2}\right)\, dx = C + \frac{x^{5}}{5} - \frac{x^{3}}{3}
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] 
-2/15
−215- \frac{2}{15} 
=
= 
-2/15
−215- \frac{2}{15} 
-2/15
Numerical answer [src] 
-0.133333333333333
-0.133333333333333
The graph
Integral of x^4-x^2 dx

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

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