Mister Exam

Other calculators

Solving integrals/ x^3-4*x

Integral of x^3-4*x dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  4              
  /              
 |               
 |  / 3      \   
 |  \x  - 4*x/ dx
 |               
/                
2
∫24(x3−4x) dx\int\limits_{2}^{4} \left(x^{3} - 4 x\right)\, dx 
Integral(x^3 - 4*x, (x, 2, 4))
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:

      ∫x3 dx=x44\int x^{3}\, dx = \frac{x^{4}}{4}

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

      ∫(−4x) dx=−4∫x dx\int \left(- 4 x\right)\, dx = - 4 \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: −2x2- 2 x^{2}

    The result is: x44−2x2\frac{x^{4}}{4} - 2 x^{2}

  2. Now simplify:

    x2(x2−8)4\frac{x^{2} \left(x^{2} - 8\right)}{4}

  3. Add the constant of integration:

    x2(x2−8)4+constant\frac{x^{2} \left(x^{2} - 8\right)}{4}+ \mathrm{constant}

The answer is:

x2(x2−8)4+constant\frac{x^{2} \left(x^{2} - 8\right)}{4}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                             
 |                             4
 | / 3      \             2   x 
 | \x  - 4*x/ dx = C - 2*x  + --
 |                            4 
/
∫(x3−4x) dx=C+x44−2x2\int \left(x^{3} - 4 x\right)\, dx = C + \frac{x^{4}}{4} - 2 x^{2}
Simplify
The graph
2.04.02.22.42.62.83.03.23.43.63.8-5050
Plot the graph f(x)
The answer [src] 
36
3636 
=
= 
36
3636 
36
Numerical answer [src] 
36.0
36.0

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

    © Mister Exam – Calculator