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Solving integrals/ -cos^2x*sinx

Integral of -cos^2x*sinx dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1                   
  /                   
 |                    
 |      2             
 |  -cos (x)*sin(x) dx
 |                    
/                     
0
$$\int\limits_{0}^{1} \sin{\left(x \right)} \left(- \cos^{2}{\left(x \right)}\right)\, dx$$ 
Integral((-cos(x)^2)*sin(x), (x, 0, 1))
Detail solution

  1. Let .

    Then let and substitute :

    1. The integral of is when :

    Now substitute back in:

  2. Add the constant of integration:

The answer is:

The answer (Indefinite) [src] 
  /                                
 |                             3   
 |     2                    cos (x)
 | -cos (x)*sin(x) dx = C + -------
 |                             3   
/
$$\int \sin{\left(x \right)} \left(- \cos^{2}{\left(x \right)}\right)\, dx = C + \frac{\cos^{3}{\left(x \right)}}{3}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
         3   
  1   cos (1)
- - + -------
  3      3
$$- \frac{1}{3} + \frac{\cos^{3}{\left(1 \right)}}{3}$$ 
=
= 
         3   
  1   cos (1)
- - + -------
  3      3
$$- \frac{1}{3} + \frac{\cos^{3}{\left(1 \right)}}{3}$$ 
-1/3 + cos(1)^3/3
Numerical answer [src] 
-0.280757131583002
-0.280757131583002

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

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