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sin(x)^3*cos(x)dx
  • How to use it?

  • Integral of d{x}:
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  • Identical expressions

  • sin(x)^ three *cos(x)dx
  • sinus of (x) cubed multiply by co sinus of e of (x)dx
  • sinus of (x) to the power of three multiply by co sinus of e of (x)dx
  • sin(x)3*cos(x)dx
  • sinx3*cosxdx
  • sin(x)³*cos(x)dx
  • sin(x) to the power of 3*cos(x)dx
  • sin(x)^3cos(x)dx
  • sin(x)3cos(x)dx
  • sinx3cosxdx
  • sinx^3cosxdx
  • Similar expressions

  • sinx^3*cosxdx

Integral of sin(x)^3*cos(x)dx dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src]
  1                    
  /                    
 |                     
 |     3               
 |  sin (x)*cos(x)*1 dx
 |                     
/                      
0                      
$$\int\limits_{0}^{1} \sin^{3}{\left(x \right)} \cos{\left(x \right)} 1\, dx$$
Integral(sin(x)^3*cos(x)*1, (x, 0, 1))
Detail solution
  1. There are multiple ways to do this integral.

    Method #1

    1. Let .

      Then let and substitute :

      1. The integral of is when :

      Now substitute back in:

    Method #2

    1. Rewrite the integrand:

    2. Let .

      Then let and substitute :

      1. Integrate term-by-term:

        1. The integral of a constant times a function is the constant times the integral of the function:

          1. The integral of is when :

          So, the result is:

        1. The integral of a constant is the constant times the variable of integration:

        The result is:

      Now substitute back in:

  2. Add the constant of integration:


The answer is:

The answer (Indefinite) [src]
  /                                 
 |                              4   
 |    3                      sin (x)
 | sin (x)*cos(x)*1 dx = C + -------
 |                              4   
/                                   
$${{\sin ^4x}\over{4}}$$
The graph
The answer [src]
   4   
sin (1)
-------
   4   
$${{\sin ^41}\over{4}}$$
=
=
   4   
sin (1)
-------
   4   
$$\frac{\sin^{4}{\left(1 \right)}}{4}$$
Numerical answer [src]
0.125341991416405
0.125341991416405
The graph
Integral of sin(x)^3*cos(x)dx dx

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