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Integral of x-3/2x^2+5x-7 dx

Limits of integration:

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The graph:

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Piecewise:

The solution

You have entered [src]
  1                        
  /                        
 |                         
 |  /       2          \   
 |  |    3*x           |   
 |  |x - ---- + 5*x - 7| dx
 |  \     2            /   
 |                         
/                          
0                          
$$\int\limits_{0}^{1} \left(\left(5 x + \left(- \frac{3 x^{2}}{2} + x\right)\right) - 7\right)\, dx$$
Integral(x - 3*x^2/2 + 5*x - 7, (x, 0, 1))
Detail solution
  1. Integrate term-by-term:

    1. Integrate term-by-term:

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

        1. The integral of is when :

        So, the result is:

      1. Integrate term-by-term:

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

          1. The integral of is when :

          So, the result is:

        1. The integral of is when :

        The result is:

      The result is:

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

    The result is:

  2. Now simplify:

  3. Add the constant of integration:


The answer is:

The answer (Indefinite) [src]
  /                                             
 |                                              
 | /       2          \                        3
 | |    3*x           |                   2   x 
 | |x - ---- + 5*x - 7| dx = C - 7*x + 3*x  - --
 | \     2            /                       2 
 |                                              
/                                               
$$\int \left(\left(5 x + \left(- \frac{3 x^{2}}{2} + x\right)\right) - 7\right)\, dx = C - \frac{x^{3}}{2} + 3 x^{2} - 7 x$$
The graph
The answer [src]
-9/2
$$- \frac{9}{2}$$
=
=
-9/2
$$- \frac{9}{2}$$
-9/2
Numerical answer [src]
-4.5
-4.5

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