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Solving integrals/ exp(y-x)*sin(y)

Integral of exp(y-x)*sin(y) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  y                 
  /                 
 |                  
 |   y - x          
 |  e     *sin(y) dx
 |                  
/                   
0
$$\int\limits_{0}^{y} e^{- x + y} \sin{\left(y \right)}\, dx$$ 
Integral(exp(y - x)*sin(y), (x, 0, y))
Detail solution

  1. The integral of a constant times a function is the constant times the integral of the function:

    1. Let .

      Then let and substitute :

      1. The integral of a constant times a function is the constant times the integral of the function:

        1. The integral of the exponential function is itself.

        So, the result is:

      Now substitute back in:

    So, the result is:

  2. Add the constant of integration:

The answer is:

The answer (Indefinite) [src] 
  /                                    
 |                                     
 |  y - x                  y - x       
 | e     *sin(y) dx = C - e     *sin(y)
 |                                     
/
$$\int e^{- x + y} \sin{\left(y \right)}\, dx = C - e^{- x + y} \sin{\left(y \right)}$$
Simplify
The answer [src] 
           y       
-sin(y) + e *sin(y)
$$e^{y} \sin{\left(y \right)} - \sin{\left(y \right)}$$ 
=
= 
           y       
-sin(y) + e *sin(y)
$$e^{y} \sin{\left(y \right)} - \sin{\left(y \right)}$$ 
-sin(y) + exp(y)*sin(y)

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

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