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(6-x)/2
Solving integrals/ (6-x)/2

Integral of (6-x)/2 dx

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The solution

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  2         
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 |  6 - x   
 |  ----- dx
 |    2     
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6
∫626−x2 dx\int\limits_{6}^{2} \frac{6 - x}{2}\, dx 
Integral(6 - x/2, (x, 6, 2))
Detail solution

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

    ∫6−x2 dx=∫(6−x) dx2\int \frac{6 - x}{2}\, dx = \frac{\int \left(6 - x\right)\, dx}{2}

    1. Integrate term-by-term:

      1. The integral of a constant is the constant times the variable of integration:

        ∫6 dx=6x\int 6\, dx = 6 x

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

        ∫(−x) dx=−∫x dx\int \left(- x\right)\, dx = - \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: −x22- \frac{x^{2}}{2}

      The result is: −x22+6x- \frac{x^{2}}{2} + 6 x

    So, the result is: −x24+3x- \frac{x^{2}}{4} + 3 x

  2. Now simplify:

    x(12−x)4\frac{x \left(12 - x\right)}{4}

  3. Add the constant of integration:

    x(12−x)4+constant\frac{x \left(12 - x\right)}{4}+ \mathrm{constant}

The answer is:

x(12−x)4+constant\frac{x \left(12 - x\right)}{4}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                       
 |                       2
 | 6 - x                x 
 | ----- dx = C + 3*x - --
 |   2                  4 
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6 x−x246\,x-{{x^2}\over{4}}
Simplify
The graph
2.06.02.53.03.54.04.55.05.5010
Plot the graph f(x)
The answer [src] 
-4
−4-4 
=
= 
-4
−4-4
Упростить
Numerical answer [src] 
-4.0
-4.0
The graph
Integral of (6-x)/2 dx

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

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