Mister Exam

Integral of 2x^2dx dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src]
  1          
  /          
 |           
 |     2     
 |  2*x *1 dx
 |           
/            
0            
012x21dx\int\limits_{0}^{1} 2 x^{2} \cdot 1\, dx
Integral(2*x^2*1, (x, 0, 1))
Detail solution
  1. The integral of a constant times a function is the constant times the integral of the function:

    2x21dx=2x2dx\int 2 x^{2} \cdot 1\, dx = 2 \int x^{2}\, dx

    1. The integral of xnx^{n} is xn+1n+1\frac{x^{n + 1}}{n + 1} when n1n \neq -1:

      x2dx=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 *1 dx = C + ----
 |                  3  
/                      
2x21dx=2x33+C\int 2 x^{2} \cdot 1\, dx = \frac{2 x^{3}}{3} + C
The graph
0.001.000.100.200.300.400.500.600.700.800.9004
The answer [src]
2/3
23{{2}\over{3}}
=
=
2/3
23\frac{2}{3}
Numerical answer [src]
0.666666666666667
0.666666666666667
The graph
Integral of 2x^2dx dx

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