Mister Exam

Other calculators

sin^4xcosx
Solving integrals/ sin^4xcosx

Integral of sin^4xcosx dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1                  
  /                  
 |                   
 |     4             
 |  sin (x)*cos(x) dx
 |                   
/                    
0
$$\int\limits_{0}^{1} \sin^{4}{\left(x \right)} \cos{\left(x \right)}\, dx$$ 
Integral(sin(x)^4*cos(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] 
  /                               
 |                            5   
 |    4                    sin (x)
 | sin (x)*cos(x) dx = C + -------
 |                            5   
/
$$\int \sin^{4}{\left(x \right)} \cos{\left(x \right)}\, dx = C + \frac{\sin^{5}{\left(x \right)}}{5}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
   5   
sin (1)
-------
   5
$$\frac{\sin^{5}{\left(1 \right)}}{5}$$ 
=
= 
   5   
sin (1)
-------
   5
$$\frac{\sin^{5}{\left(1 \right)}}{5}$$ 
sin(1)^5/5
Numerical answer [src] 
0.0843773191639561
0.0843773191639561
The graph
Integral of sin^4xcosx dx

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

    © Mister Exam – Calculator