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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
∫−33(9−x2) dx\int\limits_{-3}^{3} \left(9 - x^{2}\right)\, dx 
Integral(-x^2 + 9, (x, -3, 3))
Detail solution

  1. Integrate term-by-term:

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

      ∫9 dx=9x\int 9\, dx = 9 x

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

      ∫(−x2) dx=−∫x2 dx\int \left(- x^{2}\right)\, dx = - \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: −x33- \frac{x^{3}}{3}

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

  2. Now simplify:

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

  3. Add the constant of integration:

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

The answer is:

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

The answer (Indefinite) [src] 
  /                            
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 | \- x  + 9/ dx = C + 9*x - --
 |                           3 
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∫(9−x2) dx=C−x33+9x\int \left(9 - x^{2}\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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