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x/3
Solving integrals/ x/3

Integral of x/3 dx

Limits of integration:

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The graph:

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Piecewise:

The solution

You have entered [src] 
  5     
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 |  x   
 |  - dx
 |  3   
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2
∫25x3 dx\int\limits_{2}^{5} \frac{x}{3}\, dx 
Integral(x/3, (x, 2, 5))
Detail solution

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

    ∫x3 dx=∫x dx3\int \frac{x}{3}\, dx = \frac{\int x\, dx}{3}

    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: x26\frac{x^{2}}{6}

  2. Add the constant of integration:

    x26+constant\frac{x^{2}}{6}+ \mathrm{constant}

The answer is:

x26+constant\frac{x^{2}}{6}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /             
 |             2
 | x          x 
 | - dx = C + --
 | 3          6 
 |              
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∫x3 dx=C+x26\int \frac{x}{3}\, dx = C + \frac{x^{2}}{6}
Simplify
The graph
2.005.002.252.502.753.003.253.503.754.004.254.504.7505
Plot the graph f(x)
The answer [src] 
7/2
72\frac{7}{2} 
=
= 
7/2
72\frac{7}{2} 
7/2
Numerical answer [src] 
3.5
3.5
The graph
Integral of x/3 dx

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

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