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sin^30x*cosxdx

Integral of sin^30x*cosx dx

The solution

You have entered [src]

 pi                   
 --                   
 2                    
  /                   
 |                    
 |     30             
 |  sin  (x)*cos(x) dx
 |                    
/                     
0

$$\int\limits_{0}^{\frac{\pi}{2}} \sin^{30}{\left(x \right)} \cos{\left(x \right)}\, dx$$

Integral(sin(x)^30*cos(x), (x, 0, pi/2))

Detail solution

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

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

$\int u^{30}\, du$
1. The integral of $u^{n}$ is $\frac{u^{n + 1}}{n + 1}$ when $n \neq -1$ :
  
  $\int u^{30}\, du = \frac{u^{31}}{31}$
Now substitute $u$ back in:

$\frac{\sin^{31}{\left(x \right)}}{31}$
Add the constant of integration:

$\frac{\sin^{31}{\left(x \right)}}{31}+ \mathrm{constant}$

The answer is:

$\frac{\sin^{31}{\left(x \right)}}{31}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                 
 |                             31   
 |    30                    sin  (x)
 | sin  (x)*cos(x) dx = C + --------
 |                             31   
/

$$\int \sin^{30}{\left(x \right)} \cos{\left(x \right)}\, dx = C + \frac{\sin^{31}{\left(x \right)}}{31}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

1/31

$$\frac{1}{31}$$

1/31

$$\frac{1}{31}$$

1/31

Numerical answer [src]

0.032258064516129

0.032258064516129

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

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Identical expressions

Integral of sin^30x*cosx dx

Limits of integration:

The graph:

Piecewise:

The solution