Mister Exam

Other calculators

Solving integrals/ sin^30x*cosx

Integral of sin^30x*cosx dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
 pi                   
 --                   
 2                    
  /                   
 |                    
 |     30             
 |  sin  (x)*cos(x) dx
 |                    
/                     
0
∫0π2sin⁡30(x)cos⁡(x) dx\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

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

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

    ∫u30 du\int u^{30}\, du

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

      ∫u30 du=u3131\int u^{30}\, du = \frac{u^{31}}{31}

    Now substitute uu back in:

    sin⁡31(x)31\frac{\sin^{31}{\left(x \right)}}{31}

  2. Add the constant of integration:

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

The answer is:

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

The answer (Indefinite) [src] 
  /                                 
 |                             31   
 |    30                    sin  (x)
 | sin  (x)*cos(x) dx = C + --------
 |                             31   
/
∫sin⁡30(x)cos⁡(x) dx=C+sin⁡31(x)31\int \sin^{30}{\left(x \right)} \cos{\left(x \right)}\, dx = C + \frac{\sin^{31}{\left(x \right)}}{31}
Simplify
The graph
0.00.10.20.30.40.50.60.70.80.91.01.11.21.31.41.50.00.2
Plot the graph f(x)
The answer [src] 
1/31
131\frac{1}{31} 
=
= 
1/31
131\frac{1}{31} 
1/31
Numerical answer [src] 
0.032258064516129
0.032258064516129

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

    © Mister Exam – Calculator