Integral of x/2+1 dx

The solution

You have entered [src]

 pi           
  /           
 |            
 |  /x    \   
 |  |- + 1| dx
 |  \2    /   
 |            
/             
0

$$\int\limits_{0}^{\pi} \left(\frac{x}{2} + 1\right)\, dx$$

Integral(x/2 + 1, (x, 0, pi))

Detail solution

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

$\frac{x \left(x + 4\right)}{4}$
Add the constant of integration:

$\frac{x \left(x + 4\right)}{4}+ \mathrm{constant}$

The answer is:

$\frac{x \left(x + 4\right)}{4}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                       
 |                       2
 | /x    \              x 
 | |- + 1| dx = C + x + --
 | \2    /              4 
 |                        
/

$$\int \left(\frac{x}{2} + 1\right)\, dx = C + \frac{x^{2}}{4} + x$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

       2
     pi 
pi + ---
      4

$$\frac{\pi^{2}}{4} + \pi$$

       2
     pi 
pi + ---
      4

$$\frac{\pi^{2}}{4} + \pi$$

pi + pi^2/4

Numerical answer [src]

5.60899375386213

5.60899375386213

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+1 dx

Limits of integration:

The graph:

Piecewise:

The solution