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Solving integrals/ y+x

Integral of y+x dx

Limits of integration:

from to
v

The graph:

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Piecewise:

The solution

You have entered [src] 
      ____          
 -2*\/ -x           
     /              
    |               
    |     (y + x) dx
    |               
   /                
   -4
∫−4−2−x(x+y) dx\int\limits_{-4}^{- 2 \sqrt{- x}} \left(x + y\right)\, dx 
Integral(y + x, (x, -4, -2*sqrt(-x)))
Detail solution

  1. Integrate term-by-term:

    1. The integral of xnx^{n} is xn+1n+1\frac{x^{n + 1}}{n + 1} when n≠−1n \neq -1:

      ∫x dx=x22\int x\, dx = \frac{x^{2}}{2}

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

      ∫y dx=xy\int y\, dx = x y

    The result is: x22+xy\frac{x^{2}}{2} + x y

  2. Now simplify:

    x(x+2y)2\frac{x \left(x + 2 y\right)}{2}

  3. Add the constant of integration:

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

The answer is:

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

The answer (Indefinite) [src] 
  /                  2      
 |                  x       
 | (y + x) dx = C + -- + x*y
 |                  2       
/
∫(x+y) dx=C+x22+xy\int \left(x + y\right)\, dx = C + \frac{x^{2}}{2} + x y
Simplify
The answer [src] 
                       ____
-8 - 2*x + 4*y - 2*y*\/ -x
−2x−2y−x+4y−8- 2 x - 2 y \sqrt{- x} + 4 y - 8 
=
= 
                       ____
-8 - 2*x + 4*y - 2*y*\/ -x
−2x−2y−x+4y−8- 2 x - 2 y \sqrt{- x} + 4 y - 8 
-8 - 2*x + 4*y - 2*y*sqrt(-x)

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

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