Mister Exam

Lang:

Other calculators

How to use it?
Integral of d{x}:
Integral of 2/x^2
Integral of x/e^x
Integral of 5/x
Integral of x^1/3
Identical expressions
2x+2y- one
2x plus 2y minus 1
2x plus 2y minus one
2x+2y-1dx
Similar expressions
2x-2y-1
2x+2y+1

Integral of 2x+2y-1 dy

The solution

You have entered [src]

  1                   
  /                   
 |                    
 |  (2*x + 2*y - 1) dy
 |                    
/                     
0

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

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

Detail solution

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

$y \left(2 x + y - 1\right)$
Add the constant of integration:

$y \left(2 x + y - 1\right)+ \mathrm{constant}$

The answer is:

$y \left(2 x + y - 1\right)+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                       
 |                           2            
 | (2*x + 2*y - 1) dy = C + y  - y + 2*x*y
 |                                        
/

$$\int \left(\left(2 x + 2 y\right) - 1\right)\, dy = C + 2 x y + y^{2} - y$$

Simplify

The answer [src]

2*x

$$2 x$$

2*x

$$2 x$$

2*x

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

Other calculators

How to use it?

Identical expressions

Similar expressions

Integral of 2x+2y-1 dy

Limits of integration:

The graph:

Piecewise:

The solution