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Integral of ecosx*sinxdx dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src]
 POST_GRBEK_SMALL_pi                    
 -------------------                    
          2                             
          /                             
         |                              
         |          e*cos(x)*sin(x)*1 dx
         |                              
        /                               
        0                               
$$\int\limits_{0}^{\frac{POST_{GRBEK SMALL \pi}}{2}} e \cos{\left(x \right)} \sin{\left(x \right)} 1\, dx$$
Integral(E*cos(x)*sin(x)*1, (x, 0, POST_GRBEK_SMALL_pi/2))
Detail solution
  1. The integral of a constant times a function is the constant times the integral of the function:

    1. There are multiple ways to do this integral.

      Method #1

      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 is when :

          So, the result is:

        Now substitute back in:

      Method #2

      1. Let .

        Then let and substitute :

        1. The integral of is when :

        Now substitute back in:

    So, the result is:

  2. Add the constant of integration:


The answer is:

The answer (Indefinite) [src]
  /                                2   
 |                            e*cos (x)
 | e*cos(x)*sin(x)*1 dx = C - ---------
 |                                2    
/                                      
$$\int e \cos{\left(x \right)} \sin{\left(x \right)} 1\, dx = C - \frac{e \cos^{2}{\left(x \right)}}{2}$$
The answer [src]
     2/POST_GRBEK_SMALL_pi\
e*sin |-------------------|
      \         2         /
---------------------------
             2             
$$\frac{e \sin^{2}{\left(\frac{POST_{GRBEK SMALL \pi}}{2} \right)}}{2}$$
=
=
     2/POST_GRBEK_SMALL_pi\
e*sin |-------------------|
      \         2         /
---------------------------
             2             
$$\frac{e \sin^{2}{\left(\frac{POST_{GRBEK SMALL \pi}}{2} \right)}}{2}$$

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