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Solving integrals/ 27x

Integral of 27x dx

Limits of integration:

from to
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The graph:

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Piecewise:

The solution

You have entered [src] 
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∫0127x dx\int\limits_{0}^{1} 27 x\, dx 
Integral(27*x, (x, 0, 1))
Detail solution

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

    ∫27x dx=27∫x dx\int 27 x\, dx = 27 \int x\, dx

    1. The integral of xnx^{n} is xn+1n+1\frac{x^{n + 1}}{n + 1} when n≠−1n \neq -1:

      ∫x dx=x22\int x\, dx = \frac{x^{2}}{2}

    So, the result is: 27x22\frac{27 x^{2}}{2}

  2. Add the constant of integration:

    27x22+constant\frac{27 x^{2}}{2}+ \mathrm{constant}

The answer is:

27x22+constant\frac{27 x^{2}}{2}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                  2
 |               27*x 
 | 27*x dx = C + -----
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∫27x dx=C+27x22\int 27 x\, dx = C + \frac{27 x^{2}}{2}
Simplify
The graph
0.001.000.100.200.300.400.500.600.700.800.90050
Plot the graph f(x)
The answer [src] 
27/2
272\frac{27}{2} 
=
= 
27/2
272\frac{27}{2} 
27/2
Numerical answer [src] 
13.5
13.5

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

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