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Solving integrals/ 3*x-2

Integral of 3*x-2 dx

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The solution

You have entered [src] 
  3             
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 |  (3*x - 2) dx
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-3
∫−33(3x−2) dx\int\limits_{-3}^{3} \left(3 x - 2\right)\, dx 
Integral(3*x - 2, (x, -3, 3))
Detail solution

  1. Integrate term-by-term:

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

      ∫3x dx=3∫x dx\int 3 x\, dx = 3 \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: 3x22\frac{3 x^{2}}{2}

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

      ∫(−2) dx=−2x\int \left(-2\right)\, dx = - 2 x

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

  2. Now simplify:

    x(3x−4)2\frac{x \left(3 x - 4\right)}{2}

  3. Add the constant of integration:

    x(3x−4)2+constant\frac{x \left(3 x - 4\right)}{2}+ \mathrm{constant}

The answer is:

x(3x−4)2+constant\frac{x \left(3 x - 4\right)}{2}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                            2
 |                          3*x 
 | (3*x - 2) dx = C - 2*x + ----
 |                           2  
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∫(3x−2) dx=C+3x22−2x\int \left(3 x - 2\right)\, dx = C + \frac{3 x^{2}}{2} - 2 x
Simplify
The graph
-3.0-2.5-2.0-1.5-1.0-0.53.00.00.51.01.52.02.5-5050
Plot the graph f(x)
The answer [src] 
-12
−12-12 
=
= 
-12
−12-12 
-12
Numerical answer [src] 
-12.0
-12.0

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

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