Mister Exam

Other calculators

cos(x)×e^sin(x)
Solving integrals/ cos(x)×e^sin(x)

Integral of cos(x)×e^sin(x) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1                  
  /                  
 |                   
 |          sin(x)   
 |  cos(x)*e       dx
 |                   
/                    
0
∫01esin⁡(x)cos⁡(x) dx\int\limits_{0}^{1} e^{\sin{\left(x \right)}} \cos{\left(x \right)}\, dx 
Integral(cos(x)*E^sin(x), (x, 0, 1))
Detail solution

  1. Let u=esin⁡(x)u = e^{\sin{\left(x \right)}}.

    Then let du=esin⁡(x)cos⁡(x)dxdu = e^{\sin{\left(x \right)}} \cos{\left(x \right)} dx and substitute dudu:

    ∫1 du\int 1\, du

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

      ∫1 du=u\int 1\, du = u

    Now substitute uu back in:

    esin⁡(x)e^{\sin{\left(x \right)}}

  2. Now simplify:

    esin⁡(x)e^{\sin{\left(x \right)}}

  3. Add the constant of integration:

    esin⁡(x)+constante^{\sin{\left(x \right)}}+ \mathrm{constant}

The answer is:

esin⁡(x)+constante^{\sin{\left(x \right)}}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                               
 |                                
 |         sin(x)           sin(x)
 | cos(x)*e       dx = C + e      
 |                                
/
esin⁡xe^{\sin x}
Simplify
The graph
0.001.000.100.200.300.400.500.600.700.800.9003
Plot the graph f(x)
The answer [src] 
      sin(1)
-1 + e
esin⁡1−1e^{\sin 1}-1 
=
= 
      sin(1)
-1 + e
−1+esin⁡(1)-1 + e^{\sin{\left(1 \right)}}
Упростить
Numerical answer [src] 
1.31977682471585
1.31977682471585
The graph
Integral of cos(x)×e^sin(x) dx

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

    © Mister Exam – Calculator