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Integral of (x²/4-x/2)5(x-1)dx dx

Limits of integration:

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The graph:

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Piecewise:

The solution

You have entered [src]
  1                      
  /                      
 |                       
 |  / 2    \             
 |  |x    x|             
 |  |-- - -|*5*(x - 1) dx
 |  \4    2/             
 |                       
/                        
0                        
$$\int\limits_{0}^{1} 5 \left(\frac{x^{2}}{4} - \frac{x}{2}\right) \left(x - 1\right)\, dx$$
Integral(((x^2/4 - x/2)*5)*(x - 1), (x, 0, 1))
Detail solution
  1. There are multiple ways to do this integral.

    Method #1

    1. Let .

      Then let and substitute :

      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:

      Now substitute back in:

    Method #2

    1. Rewrite the integrand:

    2. 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 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 a constant times a function is the constant times the integral of the function:

        1. The integral of is when :

        So, the result is:

      The result is:

  2. Now simplify:

  3. Add the constant of integration:


The answer is:

The answer (Indefinite) [src]
  /                                       
 |                                       2
 | / 2    \                      / 2    \ 
 | |x    x|                      |x    x| 
 | |-- - -|*5*(x - 1) dx = C + 5*|-- - -| 
 | \4    2/                      \4    2/ 
 |                                        
/                                         
$$\int 5 \left(\frac{x^{2}}{4} - \frac{x}{2}\right) \left(x - 1\right)\, dx = C + 5 \left(\frac{x^{2}}{4} - \frac{x}{2}\right)^{2}$$
The graph
The answer [src]
5/16
$$\frac{5}{16}$$
=
=
5/16
$$\frac{5}{16}$$
5/16
Numerical answer [src]
0.3125
0.3125

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