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Solving integrals/ e^x*siny

Integral of e^x*siny dy

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
 pi             
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 |   x          
 |  E *sin(y) dy
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0
∫0πexsin⁡(y) dy\int\limits_{0}^{\pi} e^{x} \sin{\left(y \right)}\, dy 
Integral(E^x*sin(y), (y, 0, pi))
Detail solution

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

    ∫exsin⁡(y) dy=ex∫sin⁡(y) dy\int e^{x} \sin{\left(y \right)}\, dy = e^{x} \int \sin{\left(y \right)}\, dy

    1. The integral of sine is negative cosine:

      ∫sin⁡(y) dy=−cos⁡(y)\int \sin{\left(y \right)}\, dy = - \cos{\left(y \right)}

    So, the result is: −excos⁡(y)- e^{x} \cos{\left(y \right)}

  2. Add the constant of integration:

    −excos⁡(y)+constant- e^{x} \cos{\left(y \right)}+ \mathrm{constant}

The answer is:

−excos⁡(y)+constant- e^{x} \cos{\left(y \right)}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                            
 |                             
 |  x                         x
 | E *sin(y) dy = C - cos(y)*e 
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/
∫exsin⁡(y) dy=C−excos⁡(y)\int e^{x} \sin{\left(y \right)}\, dy = C - e^{x} \cos{\left(y \right)}
Simplify
The answer [src] 
   x
2*e
2ex2 e^{x} 
=
= 
   x
2*e
2ex2 e^{x} 
2*exp(x)

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

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