Integral of 2x²-2x-7 dx

The solution

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$$\int\limits_{1}^{0} \left(\left(2 x^{2} - 2 x\right) - 7\right)\, dx$$

Integral(2*x^2 - 2*x - 7, (x, 1, 0))

Detail solution

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:
    
    $\int 2 x^{2}\, dx = 2 \int x^{2}\, dx$
    1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
      
      $\int x^{2}\, dx = \frac{x^{3}}{3}$
    So, the result is: $\frac{2 x^{3}}{3}$
  1. The integral of a constant times a function is the constant times the integral of the function:
    
    $\int \left(- 2 x\right)\, dx = - 2 \int x\, dx$
    1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
      
      $\int x\, dx = \frac{x^{2}}{2}$
    So, the result is: $- x^{2}$
  The result is: $\frac{2 x^{3}}{3} - x^{2}$
1. The integral of a constant is the constant times the variable of integration:
  
  $\int \left(-7\right)\, dx = - 7 x$
The result is: $\frac{2 x^{3}}{3} - x^{2} - 7 x$
Now simplify:

$\frac{x \left(2 x^{2} - 3 x - 21\right)}{3}$
Add the constant of integration:

$\frac{x \left(2 x^{2} - 3 x - 21\right)}{3}+ \mathrm{constant}$

The answer is:

$\frac{x \left(2 x^{2} - 3 x - 21\right)}{3}+ \mathrm{constant}$

The answer (Indefinite) [src]

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 | /   2          \           2         2*x 
 | \2*x  - 2*x - 7/ dx = C - x  - 7*x + ----
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$$\int \left(\left(2 x^{2} - 2 x\right) - 7\right)\, dx = C + \frac{2 x^{3}}{3} - x^{2} - 7 x$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

22/3

$$\frac{22}{3}$$

22/3

$$\frac{22}{3}$$

22/3

Numerical answer [src]

7.33333333333333

7.33333333333333

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

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Integral of 2x²-2x-7 dx

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The solution