Integral of pi-x dx

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 pi            
  /            
 |             
 |  (pi - x) dx
 |             
/              
pi             
--             
2

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

Integral(pi - x, (x, pi/2, pi))

Detail solution

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

$\frac{x \left(- x + 2 \pi\right)}{2}$
Add the constant of integration:

$\frac{x \left(- x + 2 \pi\right)}{2}+ \mathrm{constant}$

The answer is:

$\frac{x \left(- x + 2 \pi\right)}{2}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                   2       
 |                   x        
 | (pi - x) dx = C - -- + pi*x
 |                   2        
/

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

Simplify

The graph

Plot the graph f(x)

The answer [src]

  2
pi 
---
 8

$$\frac{\pi^{2}}{8}$$

  2
pi 
---
 8

$$\frac{\pi^{2}}{8}$$

pi^2/8

Numerical answer [src]

1.23370055013617

1.23370055013617

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