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Solving integrals/ cos^2(x)*sin(x)dx

Integral of cos^2(x)*sin(x)dx dx

The solution

You have entered [src]

  1                  
  /                  
 |                   
 |     2             
 |  cos (x)*sin(x) dx
 |                   
/                    
0

$$\int\limits_{0}^{1} \sin{\left(x \right)} \cos^{2}{\left(x \right)}\, dx$$

Integral(cos(x)^2*sin(x), (x, 0, 1))

Detail solution

Let $u = \cos{\left(x \right)}$ .

Then let $du = - \sin{\left(x \right)} dx$ and substitute $- du$ :

$\int \left(- u^{2}\right)\, du$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int u^{2}\, du = - \int u^{2}\, du$
  1. The integral of $u^{n}$ is $\frac{u^{n + 1}}{n + 1}$ when $n \neq -1$ :
    
    $\int u^{2}\, du = \frac{u^{3}}{3}$
  So, the result is: $- \frac{u^{3}}{3}$
Now substitute $u$ back in:

$- \frac{\cos^{3}{\left(x \right)}}{3}$
Add the constant of integration:

$- \frac{\cos^{3}{\left(x \right)}}{3}+ \mathrm{constant}$

The answer is:

$- \frac{\cos^{3}{\left(x \right)}}{3}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                               
 |                            3   
 |    2                    cos (x)
 | cos (x)*sin(x) dx = C - -------
 |                            3   
/

$$\int \sin{\left(x \right)} \cos^{2}{\left(x \right)}\, dx = C - \frac{\cos^{3}{\left(x \right)}}{3}$$

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

The graph

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

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Identical expressions

Similar expressions

Integral of cos^2(x)*sin(x)dx dx

Limits of integration:

The graph:

Piecewise:

The solution