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x^2-6
Solving integrals/ x^2-6

Integral of x^2-6 dx

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The solution

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∫01(x2−6) dx\int\limits_{0}^{1} \left(x^{2} - 6\right)\, dx 
Integral(x^2 - 6, (x, 0, 1))
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:

      ∫(−6) dx=−6x\int \left(-6\right)\, dx = - 6 x

    The result is: x33−6x\frac{x^{3}}{3} - 6 x

  2. Now simplify:

    x(x2−18)3\frac{x \left(x^{2} - 18\right)}{3}

  3. Add the constant of integration:

    x(x2−18)3+constant\frac{x \left(x^{2} - 18\right)}{3}+ \mathrm{constant}

The answer is:

x(x2−18)3+constant\frac{x \left(x^{2} - 18\right)}{3}+ \mathrm{constant}

The answer (Indefinite) [src] 
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∫(x2−6) dx=C+x33−6x\int \left(x^{2} - 6\right)\, dx = C + \frac{x^{3}}{3} - 6 x
Simplify
The graph
0.001.000.100.200.300.400.500.600.700.800.905-10
Plot the graph f(x)
The answer [src] 
-17/3
−173- \frac{17}{3} 
=
= 
-17/3
−173- \frac{17}{3} 
-17/3
Numerical answer [src] 
-5.66666666666667
-5.66666666666667
The graph
Integral of x^2-6 dx

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

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