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Solving integrals/ cx

Integral of cx dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1       
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 |  c*x dx
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0
∫01cx dx\int\limits_{0}^{1} c x\, dx 
Integral(c*x, (x, 0, 1))
Detail solution

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

    ∫cx dx=c∫x dx\int c x\, dx = c \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: cx22\frac{c x^{2}}{2}

  2. Add the constant of integration:

    cx22+constant\frac{c x^{2}}{2}+ \mathrm{constant}

The answer is:

cx22+constant\frac{c x^{2}}{2}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                2
 |              c*x 
 | c*x dx = C + ----
 |               2  
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∫cx dx=C+cx22\int c x\, dx = C + \frac{c x^{2}}{2}
Simplify
The answer [src] 
c
-
2
c2\frac{c}{2} 
=
= 
c
-
2
c2\frac{c}{2} 
c/2

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

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