Mister Exam

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Canonical form:
x^2-11
Graphing y =:
x^2-11
Identical expressions
x^ two - eleven
x squared minus 11
x to the power of two minus eleven
x2-11
x²-11
x to the power of 2-11
x^2-11dx
Similar expressions
x^2+11

Integral of x^2-11 dx

The solution

You have entered [src]

  7             
  /             
 |              
 |  / 2     \   
 |  \x  - 11/ dx
 |              
/               
-7

$$\int\limits_{-7}^{7} \left(x^{2} - 11\right)\, dx$$

Integral(x^2 - 11, (x, -7, 7))

Detail solution

Integrate term-by-term:
1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
  
  $\int x^{2}\, dx = \frac{x^{3}}{3}$
1. The integral of a constant is the constant times the variable of integration:
  
  $\int \left(-11\right)\, dx = - 11 x$
The result is: $\frac{x^{3}}{3} - 11 x$
Now simplify:

$\frac{x \left(x^{2} - 33\right)}{3}$
Add the constant of integration:

$\frac{x \left(x^{2} - 33\right)}{3}+ \mathrm{constant}$

The answer is:

$\frac{x \left(x^{2} - 33\right)}{3}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                            
 |                            3
 | / 2     \                 x 
 | \x  - 11/ dx = C - 11*x + --
 |                           3 
/

$$\int \left(x^{2} - 11\right)\, dx = C + \frac{x^{3}}{3} - 11 x$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

224/3

$$\frac{224}{3}$$

224/3

$$\frac{224}{3}$$

224/3

Numerical answer [src]

74.6666666666667

74.6666666666667

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

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Integral of x^2-11 dx

Limits of integration:

The graph:

Piecewise:

The solution