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x^2-9
Solving integrals/ x^2-9

Integral of x^2-9 dx

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The solution

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3
∫3−3(x2−9) dx\int\limits_{3}^{-3} \left(x^{2} - 9\right)\, dx 
Integral(x^2 - 9, (x, 3, -3))
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:

      ∫(−9) dx=−9x\int \left(-9\right)\, dx = - 9 x

    The result is: x33−9x\frac{x^{3}}{3} - 9 x

  2. Now simplify:

    x(x2−27)3\frac{x \left(x^{2} - 27\right)}{3}

  3. Add the constant of integration:

    x(x2−27)3+constant\frac{x \left(x^{2} - 27\right)}{3}+ \mathrm{constant}

The answer is:

x(x2−27)3+constant\frac{x \left(x^{2} - 27\right)}{3}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                          
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∫(x2−9) dx=C+x33−9x\int \left(x^{2} - 9\right)\, dx = C + \frac{x^{3}}{3} - 9 x
Simplify
The graph
-3.0-2.5-2.0-1.5-1.0-0.53.00.00.51.01.52.02.5-5050
Plot the graph f(x)
The answer [src] 
36
3636 
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36
3636 
36
Numerical answer [src] 
36.0
36.0
The graph
Integral of x^2-9 dx

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

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