Mister Exam

Integral of x+2*y dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src]
  2             
 x              
  /             
 |              
 |  (x + 2*y) dx
 |              
/               
x               
$$\int\limits_{x}^{x^{2}} \left(x + 2 y\right)\, dx$$
Integral(x + 2*y, (x, x, x^2))
Detail solution
  1. Integrate term-by-term:

    1. The integral of is when :

    1. The integral of a constant is the constant times the variable of integration:

    The result is:

  2. Now simplify:

  3. Add the constant of integration:


The answer is:

The answer (Indefinite) [src]
  /                    2        
 |                    x         
 | (x + 2*y) dx = C + -- + 2*x*y
 |                    2         
/                               
$$\int \left(x + 2 y\right)\, dx = C + \frac{x^{2}}{2} + 2 x y$$
The answer [src]
 4    2                 
x    x                 2
-- - -- - 2*x*y + 2*y*x 
2    2                  
$$\frac{x^{4}}{2} + 2 x^{2} y - \frac{x^{2}}{2} - 2 x y$$
=
=
 4    2                 
x    x                 2
-- - -- - 2*x*y + 2*y*x 
2    2                  
$$\frac{x^{4}}{2} + 2 x^{2} y - \frac{x^{2}}{2} - 2 x y$$
x^4/2 - x^2/2 - 2*x*y + 2*y*x^2

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