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Solving integrals/ f(x)

Integral of f(x) dx

Limits of integration:

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Piecewise:

The solution

You have entered [src] 
  1       
  /       
 |        
 |  f*x dx
 |        
/         
0
∫01fx dx\int\limits_{0}^{1} f x\, dx
Simplify
Detail solution

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

    ∫fx dx=f∫x dx\int f x\, dx = f \int x\, dx

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

      ∫x dx=x22\int x\, dx = \frac{x^{2}}{2}

    So, the result is: fx22\frac{f x^{2}}{2}

  2. Add the constant of integration:

    fx22+constant\frac{f x^{2}}{2}+ \mathrm{constant}

The answer is:

fx22+constant\frac{f x^{2}}{2}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                2
 |              f*x 
 | f*x dx = C + ----
 |               2  
/
f x22{{f\,x^2}\over{2}}
Simplify
The answer [src] 
f
-
2
f2{{f}\over{2}} 
=
= 
f
-
2
f2\frac{f}{2}
Simplify

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

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