Integral of x-2y dx

You have entered [src]

  1             
  /             
 |              
 |  (x - 2*y) dx
 |              
/               
0

$$\int\limits_{0}^{1} \left(x - 2 y\right)\, dx$$

Integral(x - 2*y, (x, 0, 1))

Detail solution

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

$\frac{x \left(x - 4 y\right)}{2}$
Add the constant of integration:

$\frac{x \left(x - 4 y\right)}{2}+ \mathrm{constant}$

The answer is:

$\frac{x \left(x - 4 y\right)}{2}+ \mathrm{constant}$

The answer (Indefinite) [src]

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

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

Simplify

The answer [src]

1/2 - 2*y

$$\frac{1}{2} - 2 y$$

1/2 - 2*y

$$\frac{1}{2} - 2 y$$

1/2 - 2*y

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