Mister Exam

Other calculators

x^2/4
Solving integrals/ x^2/4

Integral of x^2/4 dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1      
  /      
 |       
 |   2   
 |  x    
 |  -- dx
 |  4    
 |       
/        
0
∫01x24 dx\int\limits_{0}^{1} \frac{x^{2}}{4}\, dx 
Integral(x^2/4, (x, 0, 1))
Detail solution

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

    ∫x24 dx=∫x2 dx4\int \frac{x^{2}}{4}\, dx = \frac{\int x^{2}\, dx}{4}

    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: x312\frac{x^{3}}{12}

  2. Add the constant of integration:

    x312+constant\frac{x^{3}}{12}+ \mathrm{constant}

The answer is:

x312+constant\frac{x^{3}}{12}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /              
 |               
 |  2           3
 | x           x 
 | -- dx = C + --
 | 4           12
 |               
/
∫x24 dx=C+x312\int \frac{x^{2}}{4}\, dx = C + \frac{x^{3}}{12}
Simplify
The graph
0.001.000.100.200.300.400.500.600.700.800.900.000.50
Plot the graph f(x)
The answer [src] 
1/12
112\frac{1}{12} 
=
= 
1/12
112\frac{1}{12} 
1/12
Numerical answer [src] 
0.0833333333333333
0.0833333333333333
The graph
Integral of x^2/4 dx

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

    © Mister Exam – Calculator