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Solving integrals/ ax

Integral of ax dx

Limits of integration:

from to
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The graph:

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Piecewise:

The solution

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

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

    ∫ax dx=a∫x dx\int a x\, dx = a \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: ax22\frac{a x^{2}}{2}

  2. Add the constant of integration:

    ax22+constant\frac{a x^{2}}{2}+ \mathrm{constant}

The answer is:

ax22+constant\frac{a x^{2}}{2}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                2
 |              a*x 
 | a*x dx = C + ----
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∫ax dx=C+ax22\int a x\, dx = C + \frac{a x^{2}}{2}
Simplify
The answer [src] 
a
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2
a2\frac{a}{2} 
=
= 
a
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2
a2\frac{a}{2} 
a/2

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

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