Mister Exam

Other calculators

Solving integrals/ x^3-27

Integral of x^3-27 dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  3             
  /             
 |              
 |  / 3     \   
 |  \x  - 27/ dx
 |              
/               
0
$$\int\limits_{0}^{3} \left(x^{3} - 27\right)\, dx$$ 
Integral(x^3 - 27, (x, 0, 3))
Detail solution

  1. Integrate term-by-term:

    1. The integral of is when :

    1. The integral of a constant is the constant times the variable of integration:

    The result is:

  2. Now simplify:

  3. Add the constant of integration:

The answer is:

The answer (Indefinite) [src] 
  /                            
 |                            4
 | / 3     \                 x 
 | \x  - 27/ dx = C - 27*x + --
 |                           4 
/
$$\int \left(x^{3} - 27\right)\, dx = C + \frac{x^{4}}{4} - 27 x$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
-243/4
$$- \frac{243}{4}$$ 
=
= 
-243/4
$$- \frac{243}{4}$$ 
-243/4
Numerical answer [src] 
-60.75
-60.75

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

    © Mister Exam – Calculator