Mister Exam

Other calculators

2*x^2
Solving integrals/ 2*x^2

Integral of 2*x^2 dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1        
  /        
 |         
 |     2   
 |  2*x  dx
 |         
/          
0
∫012x2 dx\int\limits_{0}^{1} 2 x^{2}\, dx 
Integral(2*x^2, (x, 0, 1))
Detail solution

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

    ∫2x2 dx=2∫x2 dx\int 2 x^{2}\, dx = 2 \int x^{2}\, dx

    1. The integral of xnx^{n} is xn+1n+1\frac{x^{n + 1}}{n + 1} when n≠−1n \neq -1:

      ∫x2 dx=x33\int x^{2}\, dx = \frac{x^{3}}{3}

    So, the result is: 2x33\frac{2 x^{3}}{3}

  2. Add the constant of integration:

    2x33+constant\frac{2 x^{3}}{3}+ \mathrm{constant}

The answer is:

2x33+constant\frac{2 x^{3}}{3}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                  
 |                  3
 |    2          2*x 
 | 2*x  dx = C + ----
 |                3  
/
∫2x2 dx=C+2x33\int 2 x^{2}\, dx = C + \frac{2 x^{3}}{3}
Simplify
The graph
0.001.000.100.200.300.400.500.600.700.800.9004
Plot the graph f(x)
The answer [src] 
2/3
23\frac{2}{3} 
=
= 
2/3
23\frac{2}{3} 
2/3
Numerical answer [src] 
0.666666666666667
0.666666666666667
The graph
Integral of 2*x^2 dx

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

    © Mister Exam – Calculator