Mister Exam

Other calculators

3*x^3
Solving integrals/ 3*x^3

Integral of 3*x^3 dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1        
  /        
 |         
 |     3   
 |  3*x  dx
 |         
/          
0
∫013x3 dx\int\limits_{0}^{1} 3 x^{3}\, dx 
Integral(3*x^3, (x, 0, 1))
Detail solution

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

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

    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}

    So, the result is: 3x44\frac{3 x^{4}}{4}

  2. Add the constant of integration:

    3x44+constant\frac{3 x^{4}}{4}+ \mathrm{constant}

The answer is:

3x44+constant\frac{3 x^{4}}{4}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                  
 |                  4
 |    3          3*x 
 | 3*x  dx = C + ----
 |                4  
/
∫3x3 dx=C+3x44\int 3 x^{3}\, dx = C + \frac{3 x^{4}}{4}
Simplify
The graph
0.001.000.100.200.300.400.500.600.700.800.9005
Plot the graph f(x)
The answer [src] 
3/4
34\frac{3}{4} 
=
= 
3/4
34\frac{3}{4} 
3/4
Numerical answer [src] 
0.75
0.75
The graph
Integral of 3*x^3 dx

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

    © Mister Exam – Calculator