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Integral of d{x}:
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Graphing y =:
-x^2+4x-3
Canonical form:
-x^2+4x-3
Identical expressions
-x^ two +4x- three
minus x squared plus 4x minus 3
minus x to the power of two plus 4x minus three
-x2+4x-3
-x²+4x-3
-x to the power of 2+4x-3
-x^2+4x-3dx
Similar expressions
x^2+4x-3
-x^2+4x+3
-x^2-4x-3

Solving integrals/ -x^2+4x-3

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

The solution

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

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

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

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:
    
    $\int 4 x\, dx = 4 \int x\, dx$
    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:
  
  $\int \left(-3\right)\, dx = - 3 x$
The result is: $- \frac{x^{3}}{3} + 2 x^{2} - 3 x$
Now simplify:

$\frac{x \left(- x^{2} + 6 x - 9\right)}{3}$
Add the constant of integration:

$\frac{x \left(- x^{2} + 6 x - 9\right)}{3}+ \mathrm{constant}$

The answer is:

$\frac{x \left(- x^{2} + 6 x - 9\right)}{3}+ \mathrm{constant}$

The answer (Indefinite) [src]

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

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

Simplify

The graph

Plot the graph f(x)

The answer [src]

4/3

$$\frac{4}{3}$$

4/3

$$\frac{4}{3}$$

4/3

Numerical answer [src]

1.33333333333333

1.33333333333333

The graph

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

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Identical expressions

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

Limits of integration:

The graph:

Piecewise:

The solution