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8-2x^2
Solving integrals/ 8-2x^2

Integral of 8-2x^2 dx

Limits of integration:

from to
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The graph:

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Piecewise:

The solution

You have entered [src] 
  2              
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 |  /       2\   
 |  \8 - 2*x / dx
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-2
∫−22(−2x2+8) dx\int\limits_{-2}^{2} \left(- 2 x^{2} + 8\right)\, dx
Simplify
Detail solution

  1. Integrate term-by-term:

    1. The integral of a constant is the constant times the variable of integration:

      ∫8 dx=8x\int 8\, dx = 8 x

    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: −2x33+8x- \frac{2 x^{3}}{3} + 8 x

  2. Now simplify:

    2x(12−x2)3\frac{2 x \left(12 - x^{2}\right)}{3}

  3. Add the constant of integration:

    2x(12−x2)3+constant\frac{2 x \left(12 - x^{2}\right)}{3}+ \mathrm{constant}

The answer is:

2x(12−x2)3+constant\frac{2 x \left(12 - x^{2}\right)}{3}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                              
 |                              3
 | /       2\                2*x 
 | \8 - 2*x / dx = C + 8*x - ----
 |                            3  
/
8 x−2 x338\,x-{{2\,x^3}\over{3}}
Simplify
The graph
-2.0-1.5-1.0-0.52.00.00.51.01.5-2525
Plot the graph f(x)
The answer [src] 
64/3
643{{64}\over{3}} 
=
= 
64/3
643\frac{64}{3}
Simplify
Numerical answer [src] 
21.3333333333333
21.3333333333333
The graph
Integral of 8-2x^2 dx

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

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