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Solving integrals/ (1/3x-4x^3)

Integral of (1/3x-4x^3) dx

Limits of integration:

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The graph:

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Piecewise:

The solution

You have entered [src] 
  4              
  /              
 |               
 |  /x      3\   
 |  |- - 4*x | dx
 |  \3       /   
 |               
/                
-3
$$\int\limits_{-3}^{4} \left(- 4 x^{3} + \frac{x}{3}\right)\, dx$$ 
Integral(x/3 - 4*x^3, (x, -3, 4))
Detail solution

  1. Integrate term-by-term:

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

      1. The integral of is when :

      So, the result is:

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

      1. The integral of is when :

      So, the result is:

    The result is:

  2. Add the constant of integration:

The answer is:

The answer (Indefinite) [src] 
  /                           
 |                           2
 | /x      3\           4   x 
 | |- - 4*x | dx = C - x  + --
 | \3       /               6 
 |                            
/
$$\int \left(- 4 x^{3} + \frac{x}{3}\right)\, dx = C - x^{4} + \frac{x^{2}}{6}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
-1043/6
$$- \frac{1043}{6}$$ 
=
= 
-1043/6
$$- \frac{1043}{6}$$ 
-1043/6
Numerical answer [src] 
-173.833333333333
-173.833333333333

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

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