Mister Exam

Other calculators

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

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

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1                   
  /                   
 |                    
 |   -cos(x)          
 |  e       *sin(x) dx
 |                    
/                     
0
$$\int\limits_{0}^{1} e^{- \cos{\left(x \right)}} \sin{\left(x \right)}\, dx$$ 
Integral(exp(-cos(x))*sin(x), (x, 0, 1))
Detail solution

  1. Let .

    Then let and substitute :

    1. The integral of the exponential function is itself.

    Now substitute back in:

  2. Add the constant of integration:

The answer is:

The answer (Indefinite) [src] 
  /                                 
 |                                  
 |  -cos(x)                  -cos(x)
 | e       *sin(x) dx = C + e       
 |                                  
/
$$\int e^{- \cos{\left(x \right)}} \sin{\left(x \right)}\, dx = C + e^{- \cos{\left(x \right)}}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
   -1    -cos(1)
- e   + e
$$- \frac{1}{e} + e^{- \cos{\left(1 \right)}}$$ 
=
= 
   -1    -cos(1)
- e   + e
$$- \frac{1}{e} + e^{- \cos{\left(1 \right)}}$$ 
-exp(-1) + exp(-cos(1))
Numerical answer [src] 
0.214692669611866
0.214692669611866
The graph
Integral of exp(-cos(x))*sin(x) dx

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

    © Mister Exam – Calculator