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Solving integrals/ (x-3)/2

Integral of (x-3)/2 dx

Limits of integration:

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The graph:

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Piecewise:

The solution

You have entered [src] 
  1         
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 |  x - 3   
 |  ----- dx
 |    2     
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0
∫01x−32 dx\int\limits_{0}^{1} \frac{x - 3}{2}\, dx 
Integral((x - 3)/2, (x, 0, 1))
Detail solution

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

    ∫x−32 dx=∫(x−3) dx2\int \frac{x - 3}{2}\, dx = \frac{\int \left(x - 3\right)\, dx}{2}

    1. Integrate term-by-term:

      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}

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

        ∫(−3) dx=−3x\int \left(-3\right)\, dx = - 3 x

      The result is: x22−3x\frac{x^{2}}{2} - 3 x

    So, the result is: x24−3x2\frac{x^{2}}{4} - \frac{3 x}{2}

  2. Now simplify:

    x(x−6)4\frac{x \left(x - 6\right)}{4}

  3. Add the constant of integration:

    x(x−6)4+constant\frac{x \left(x - 6\right)}{4}+ \mathrm{constant}

The answer is:

x(x−6)4+constant\frac{x \left(x - 6\right)}{4}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                       
 |                       2
 | x - 3          3*x   x 
 | ----- dx = C - --- + --
 |   2             2    4 
 |                        
/
∫x−32 dx=C+x24−3x2\int \frac{x - 3}{2}\, dx = C + \frac{x^{2}}{4} - \frac{3 x}{2}
Simplify
The graph
0.001.000.100.200.300.400.500.600.700.800.902-2
Plot the graph f(x)
The answer [src] 
-5/4
−54- \frac{5}{4} 
=
= 
-5/4
−54- \frac{5}{4} 
-5/4
Numerical answer [src] 
-1.25
-1.25

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

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