Mister Exam

Lang:

Other calculators

How to use it?
Integral of d{x}:
Integral of e^(x^2)
Integral of sin(x)^3
Integral of √(x^2+1)
Integral of cos(5x)
Canonical form:
-x^2-3x+4
Graphing y =:
-x^2-3x+4
Identical expressions
-x^ two -3x+ four
minus x squared minus 3x plus 4
minus x to the power of two minus 3x plus four
-x2-3x+4
-x²-3x+4
-x to the power of 2-3x+4
-x^2-3x+4dx
Similar expressions
x^2-3x+4
-x^2-3x-4
-x^2+3x+4

Integral of -x^2-3x+4 dx

The solution

You have entered [src]

  1                    
  /                    
 |                     
 |  /   2          \   
 |  \- x  - 3*x + 4/ dx
 |                     
/                      
0

$$\int\limits_{0}^{1} \left(\left(- x^{2} - 3 x\right) + 4\right)\, dx$$

Integral(-x^2 - 3*x + 4, (x, 0, 1))

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

$\frac{x \left(- 2 x^{2} - 9 x + 24\right)}{6}$
Add the constant of integration:

$\frac{x \left(- 2 x^{2} - 9 x + 24\right)}{6}+ \mathrm{constant}$

The answer is:

$\frac{x \left(- 2 x^{2} - 9 x + 24\right)}{6}+ \mathrm{constant}$

The answer (Indefinite) [src]

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

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

Simplify

The graph

Plot the graph f(x)

The answer [src]

13/6

$$\frac{13}{6}$$

13/6

$$\frac{13}{6}$$

13/6

Numerical answer [src]

2.16666666666667

2.16666666666667

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

Other calculators

How to use it?

Identical expressions

Similar expressions

Integral of -x^2-3x+4 dx

Limits of integration:

The graph:

Piecewise:

The solution