Mister Exam

Other calculators

x^3-2
Solving integrals/ x^3-2

Integral of x^3-2 dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  3            
  /            
 |             
 |  / 3    \   
 |  \x  - 2/ dx
 |             
/              
0
∫03(x3−2) dx\int\limits_{0}^{3} \left(x^{3} - 2\right)\, dx 
Integral(x^3 - 1*2, (x, 0, 3))
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 is the constant times the variable of integration:

      ∫((−1)2) dx=−2x\int \left(\left(-1\right) 2\right)\, dx = - 2 x

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

  2. Now simplify:

    x(x3−8)4\frac{x \left(x^{3} - 8\right)}{4}

  3. Add the constant of integration:

    x(x3−8)4+constant\frac{x \left(x^{3} - 8\right)}{4}+ \mathrm{constant}

The answer is:

x(x3−8)4+constant\frac{x \left(x^{3} - 8\right)}{4}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                          
 |                          4
 | / 3    \                x 
 | \x  - 2/ dx = C - 2*x + --
 |                         4 
/
x44−2 x{{x^4}\over{4}}-2\,x
Simplify
The graph
0.003.000.250.500.751.001.251.501.752.002.252.502.7550-25
Plot the graph f(x)
The answer [src] 
57/4
574{{57}\over{4}} 
=
= 
57/4
574\frac{57}{4}
Simplify
Numerical answer [src] 
14.25
14.25
The graph
Integral of x^3-2 dx

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

    © Mister Exam – Calculator