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

Integral of x^2-x^4 dx

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The solution

You have entered [src] 
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0
∫01(−x4+x2) dx\int\limits_{0}^{1} \left(- x^{4} + x^{2}\right)\, dx 
Integral(x^2 - x^4, (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:

      ∫(−x4) dx=−∫x4 dx\int \left(- x^{4}\right)\, dx = - \int x^{4}\, dx

      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}

      So, the result is: −x55- \frac{x^{5}}{5}

    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}

    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] 
  /                          
 |                     5    3
 | / 2    4\          x    x 
 | \x  - x / dx = C - -- + --
 |                    5    3 
/
x33−x55{{x^3}\over{3}}-{{x^5}\over{5}}
Simplify
The graph
0.001.000.100.200.300.400.500.600.700.800.900.000.50
Plot the graph f(x)
The answer [src] 
2/15
215{{2}\over{15}} 
=
= 
2/15
215\frac{2}{15}
Simplify
Numerical answer [src] 
0.133333333333333
0.133333333333333
The graph
Integral of x^2-x^4 dx

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

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