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Graphing y =:
-x²+5x-4
Identical expressions
-x²+5x- four
minus x² plus 5x minus 4
minus x² plus 5x minus four
-x²+5x-4dx
Similar expressions
-x²+5x+4
x²+5x-4
-x²-5x-4

Solving integrals/ -x²+5x-4

Integral of -x²+5x-4 dx

The solution

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  4                    
  /                    
 |                     
 |  /   2          \   
 |  \- x  + 5*x - 4/ dx
 |                     
/                      
1

$$\int\limits_{1}^{4} \left(\left(- x^{2} + 5 x\right) - 4\right)\, dx$$

Integral(-x^2 + 5*x - 4, (x, 1, 4))

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:
    
    $\int 5 x\, dx = 5 \int x\, dx$
    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: $\frac{5 x^{2}}{2}$
  The result is: $- \frac{x^{3}}{3} + \frac{5 x^{2}}{2}$
1. The integral of a constant is the constant times the variable of integration:
  
  $\int \left(-4\right)\, dx = - 4 x$
The result is: $- \frac{x^{3}}{3} + \frac{5 x^{2}}{2} - 4 x$
Now simplify:

$\frac{x \left(- 2 x^{2} + 15 x - 24\right)}{6}$
Add the constant of integration:

$\frac{x \left(- 2 x^{2} + 15 x - 24\right)}{6}+ \mathrm{constant}$

The answer is:

$\frac{x \left(- 2 x^{2} + 15 x - 24\right)}{6}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                         
 |                                  3      2
 | /   2          \                x    5*x 
 | \- x  + 5*x - 4/ dx = C - 4*x - -- + ----
 |                                 3     2  
/

$$\int \left(\left(- x^{2} + 5 x\right) - 4\right)\, dx = C - \frac{x^{3}}{3} + \frac{5 x^{2}}{2} - 4 x$$

Simplify

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Plot the graph f(x)

The answer [src]

9/2

$$\frac{9}{2}$$

9/2

$$\frac{9}{2}$$

9/2

Numerical answer [src]

4.5

4.5

The graph

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

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Integral of -x²+5x-4 dx

Limits of integration:

The graph:

Piecewise:

The solution