Integral of 5(x-2) dt

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 |  5*(x - 2) dx
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$$\int\limits_{0}^{1} 5 \left(x - 2\right)\, dx$$

Integral(5*(x - 2), (x, 0, 1))

Detail solution

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

$\int 5 \left(x - 2\right)\, dx = 5 \int \left(x - 2\right)\, dx$
1. Integrate term-by-term:
  1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
    
    $\int x\, dx = \frac{x^{2}}{2}$
  1. The integral of a constant is the constant times the variable of integration:
    
    $\int \left(-2\right)\, dx = - 2 x$
  The result is: $\frac{x^{2}}{2} - 2 x$
So, the result is: $\frac{5 x^{2}}{2} - 10 x$
Now simplify:

$\frac{5 x \left(x - 4\right)}{2}$
Add the constant of integration:

$\frac{5 x \left(x - 4\right)}{2}+ \mathrm{constant}$

The answer is:

$\frac{5 x \left(x - 4\right)}{2}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                             2
 |                           5*x 
 | 5*(x - 2) dx = C - 10*x + ----
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$$\int 5 \left(x - 2\right)\, dx = C + \frac{5 x^{2}}{2} - 10 x$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

-15/2

$$- \frac{15}{2}$$

-15/2

$$- \frac{15}{2}$$

-15/2

Numerical answer [src]

-7.5

-7.5

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