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Solving integrals/ x^2-11

Integral of x^2-11 dx

Limits of integration:

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v

The graph:

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Piecewise:

The solution

You have entered [src] 
  7             
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 |  \x  - 11/ dx
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-7
∫−77(x2−11) dx\int\limits_{-7}^{7} \left(x^{2} - 11\right)\, dx 
Integral(x^2 - 11, (x, -7, 7))
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:

      ∫x2 dx=x33\int x^{2}\, dx = \frac{x^{3}}{3}

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

      ∫(−11) dx=−11x\int \left(-11\right)\, dx = - 11 x

    The result is: x33−11x\frac{x^{3}}{3} - 11 x

  2. Now simplify:

    x(x2−33)3\frac{x \left(x^{2} - 33\right)}{3}

  3. Add the constant of integration:

    x(x2−33)3+constant\frac{x \left(x^{2} - 33\right)}{3}+ \mathrm{constant}

The answer is:

x(x2−33)3+constant\frac{x \left(x^{2} - 33\right)}{3}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                            
 |                            3
 | / 2     \                 x 
 | \x  - 11/ dx = C - 11*x + --
 |                           3 
/
∫(x2−11) dx=C+x33−11x\int \left(x^{2} - 11\right)\, dx = C + \frac{x^{3}}{3} - 11 x
Simplify
The graph
70123456-7-6-5-4-3-2-1-100100
Plot the graph f(x)
The answer [src] 
224/3
2243\frac{224}{3} 
=
= 
224/3
2243\frac{224}{3} 
224/3
Numerical answer [src] 
74.6666666666667
74.6666666666667

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

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