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Solving integrals/ x^2+11

Integral of x^2+11 dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
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∫02(x2+11) dx\int\limits_{0}^{2} \left(x^{2} + 11\right)\, dx 
Integral(x^2 + 11, (x, 0, 2))
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 11\, 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] 
  /                            
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 | / 2     \                 x 
 | \x  + 11/ dx = C + 11*x + --
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∫(x2+11) dx=C+x33+11x\int \left(x^{2} + 11\right)\, dx = C + \frac{x^{3}}{3} + 11 x
Simplify
The graph
0.02.00.20.40.60.81.01.21.41.61.8050
Plot the graph f(x)
The answer [src] 
74/3
743\frac{74}{3} 
=
= 
74/3
743\frac{74}{3} 
74/3
Numerical answer [src] 
24.6666666666667
24.6666666666667

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

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