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Solving integrals/ cosxsin^2xdx

Integral of cosxsin^2xdx dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
 5/2                 
  /                  
 |                   
 |            2      
 |  cos(x)*sin (x) dx
 |                   
/                    
0
∫052sin⁡2(x)cos⁡(x) dx\int\limits_{0}^{\frac{5}{2}} \sin^{2}{\left(x \right)} \cos{\left(x \right)}\, dx 
Integral(cos(x)*sin(x)^2, (x, 0, 5/2))
Detail solution

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

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

    ∫u2 du\int u^{2}\, du

    1. The integral of unu^{n} is un+1n+1\frac{u^{n + 1}}{n + 1} when n≠−1n \neq -1:

      ∫u2 du=u33\int u^{2}\, du = \frac{u^{3}}{3}

    Now substitute uu back in:

    sin⁡3(x)3\frac{\sin^{3}{\left(x \right)}}{3}

  2. Add the constant of integration:

    sin⁡3(x)3+constant\frac{\sin^{3}{\left(x \right)}}{3}+ \mathrm{constant}

The answer is:

sin⁡3(x)3+constant\frac{\sin^{3}{\left(x \right)}}{3}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                               
 |                            3   
 |           2             sin (x)
 | cos(x)*sin (x) dx = C + -------
 |                            3   
/
∫sin⁡2(x)cos⁡(x) dx=C+sin⁡3(x)3\int \sin^{2}{\left(x \right)} \cos{\left(x \right)}\, dx = C + \frac{\sin^{3}{\left(x \right)}}{3}
Simplify
The graph
0.002.500.250.500.751.001.251.501.752.002.251.0-1.0
Plot the graph f(x)
The answer [src] 
   3     
sin (5/2)
---------
    3
sin⁡3(52)3\frac{\sin^{3}{\left(\frac{5}{2} \right)}}{3} 
=
= 
   3     
sin (5/2)
---------
    3
sin⁡3(52)3\frac{\sin^{3}{\left(\frac{5}{2} \right)}}{3} 
sin(5/2)^3/3
Numerical answer [src] 
0.0714513712947609
0.0714513712947609

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

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