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Solving integrals/ 12*x^2

Integral of 12*x^2 dx

Limits of integration:

from to
v

The graph:

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Piecewise:

The solution

You have entered [src] 
  2         
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 |      2   
 |  12*x  dx
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-1
∫−1212x2 dx\int\limits_{-1}^{2} 12 x^{2}\, dx 
Integral(12*x^2, (x, -1, 2))
Detail solution

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

    ∫12x2 dx=12∫x2 dx\int 12 x^{2}\, dx = 12 \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: 4x34 x^{3}

  2. Add the constant of integration:

    4x3+constant4 x^{3}+ \mathrm{constant}

The answer is:

4x3+constant4 x^{3}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                   
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 |     2             3
 | 12*x  dx = C + 4*x 
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∫12x2 dx=C+4x3\int 12 x^{2}\, dx = C + 4 x^{3}
Simplify
The graph
-1.00-0.75-0.50-0.252.000.000.250.500.751.001.251.501.75-5050
Plot the graph f(x)
The answer [src] 
36
3636 
=
= 
36
3636 
36
Numerical answer [src] 
36.0
36.0

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

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