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Similar expressions
7x/2+x^2/2

Integral of 7x/2-x^2/2 dx

The solution

You have entered [src]

  2              
  /              
 |               
 |  /       2\   
 |  |7*x   x |   
 |  |--- - --| dx
 |  \ 2    2 /   
 |               
/                
0

$$\int\limits_{0}^{2} \left(- \frac{x^{2}}{2} + \frac{7 x}{2}\right)\, dx$$

Integral((7*x)/2 - x^2/2, (x, 0, 2))

Detail solution

Integrate term-by-term:
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \left(- \frac{x^{2}}{2}\right)\, dx = - \frac{\int x^{2}\, dx}{2}$
  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: $- \frac{x^{3}}{6}$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \frac{7 x}{2}\, dx = \frac{\int 7 x\, dx}{2}$
  1. The integral of a constant times a function is the constant times the integral of the function:
    
    $\int 7 x\, dx = 7 \int x\, dx$
    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: $\frac{7 x^{2}}{2}$
  So, the result is: $\frac{7 x^{2}}{4}$
The result is: $- \frac{x^{3}}{6} + \frac{7 x^{2}}{4}$
Now simplify:

$\frac{x^{2} \left(21 - 2 x\right)}{12}$
Add the constant of integration:

$\frac{x^{2} \left(21 - 2 x\right)}{12}+ \mathrm{constant}$

The answer is:

$\frac{x^{2} \left(21 - 2 x\right)}{12}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                             
 |                              
 | /       2\           3      2
 | |7*x   x |          x    7*x 
 | |--- - --| dx = C - -- + ----
 | \ 2    2 /          6     4  
 |                              
/

$$\int \left(- \frac{x^{2}}{2} + \frac{7 x}{2}\right)\, dx = C - \frac{x^{3}}{6} + \frac{7 x^{2}}{4}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

17/3

$$\frac{17}{3}$$

17/3

$$\frac{17}{3}$$

17/3

Numerical answer [src]

5.66666666666667

5.66666666666667

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

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Integral of 7x/2-x^2/2 dx

Limits of integration:

The graph:

Piecewise:

The solution