Mister Exam

Lang:

Other calculators

How to use it?
Integral of d{x}:
Integral of cosx
Integral of (3-sin(x))/(2cos(x)+3tan(x))
Integral of x^3(e^x^2)
Integral of 1/(x^2+2x+10)
Graphing y =:
x^2+4x-7
Identical expressions
x^ two +4x- seven
x squared plus 4x minus 7
x to the power of two plus 4x minus seven
x2+4x-7
x²+4x-7
x to the power of 2+4x-7
x^2+4x-7dx
Similar expressions
x^2-4x-7
x^2+4x+7

Integral of x^2+4x-7 dx

The solution

You have entered [src]

  13                  
  --                  
  10                  
   /                  
  |                   
  |  / 2          \   
  |  \x  + 4*x - 7/ dx
  |                   
 /                    
-53                   
----                  
 10

$$\int\limits_{- \frac{53}{10}}^{\frac{13}{10}} \left(\left(x^{2} + 4 x\right) - 7\right)\, dx$$

Integral(x^2 + 4*x - 7, (x, -53/10, 13/10))

Detail solution

Integrate term-by-term:
1. 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 times a function is the constant times the integral of the function:
    
    $\int 4 x\, dx = 4 \int x\, dx$
    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: $2 x^{2}$
  The result is: $\frac{x^{3}}{3} + 2 x^{2}$
1. The integral of a constant is the constant times the variable of integration:
  
  $\int \left(-7\right)\, dx = - 7 x$
The result is: $\frac{x^{3}}{3} + 2 x^{2} - 7 x$
Now simplify:

$\frac{x \left(x^{2} + 6 x - 21\right)}{3}$
Add the constant of integration:

$\frac{x \left(x^{2} + 6 x - 21\right)}{3}+ \mathrm{constant}$

The answer is:

$\frac{x \left(x^{2} + 6 x - 21\right)}{3}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                       
 |                                       3
 | / 2          \                   2   x 
 | \x  + 4*x - 7/ dx = C - 7*x + 2*x  + --
 |                                      3 
/

$$\int \left(\left(x^{2} + 4 x\right) - 7\right)\, dx = C + \frac{x^{3}}{3} + 2 x^{2} - 7 x$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

-24321 
-------
  500

$$- \frac{24321}{500}$$

-24321 
-------
  500

$$- \frac{24321}{500}$$

-24321/500

Numerical answer [src]

-48.642

-48.642

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

Other calculators

How to use it?

Identical expressions

Similar expressions

Integral of x^2+4x-7 dx

Limits of integration:

The graph:

Piecewise:

The solution