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  • Identical expressions

  • thirty-two *sin^ four (x)*cos^ two (x)
  • 32 multiply by sinus of to the power of 4(x) multiply by co sinus of e of squared (x)
  • thirty minus two multiply by sinus of to the power of four (x) multiply by co sinus of e of to the power of two (x)
  • 32*sin4(x)*cos2(x)
  • 32*sin4x*cos2x
  • 32*sin⁴(x)*cos²(x)
  • 32*sin to the power of 4(x)*cos to the power of 2(x)
  • 32sin^4(x)cos^2(x)
  • 32sin4(x)cos2(x)
  • 32sin4xcos2x
  • 32sin^4xcos^2x
  • 32*sin^4(x)*cos^2(x)dx
Solving integrals/ 32*sin^4(x)*cos^2(x)

Integral of 32*sin^4(x)*cos^2(x) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
 pi                      
 --                      
 6                       
  /                      
 |                       
 |        4       2      
 |  32*sin (x)*cos (x) dx
 |                       
/                        
0
$$\int\limits_{0}^{\frac{\pi}{6}} 32 \sin^{4}{\left(x \right)} \cos^{2}{\left(x \right)}\, dx$$ 
Integral((32*sin(x)^4)*cos(x)^2, (x, 0, pi/6))
The answer (Indefinite) [src] 
  /                                                                                                                                                            
 |                                                                                                     3       3                                               
 |       4       2                  5                    6             6           5             16*cos (x)*sin (x)          2       4             4       2   
 | 32*sin (x)*cos (x) dx = C - 2*cos (x)*sin(x) + 2*x*cos (x) + 2*x*sin (x) + 2*sin (x)*cos(x) - ------------------ + 6*x*cos (x)*sin (x) + 6*x*cos (x)*sin (x)
 |                                                                                                       3                                                     
/
$$\int 32 \sin^{4}{\left(x \right)} \cos^{2}{\left(x \right)}\, dx = C + 2 x \sin^{6}{\left(x \right)} + 6 x \sin^{4}{\left(x \right)} \cos^{2}{\left(x \right)} + 6 x \sin^{2}{\left(x \right)} \cos^{4}{\left(x \right)} + 2 x \cos^{6}{\left(x \right)} + 2 \sin^{5}{\left(x \right)} \cos{\left(x \right)} - \frac{16 \sin^{3}{\left(x \right)} \cos^{3}{\left(x \right)}}{3} - 2 \sin{\left(x \right)} \cos^{5}{\left(x \right)}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
    ___     
  \/ 3    pi
- ----- + --
    2     3
$$- \frac{\sqrt{3}}{2} + \frac{\pi}{3}$$ 
=
= 
    ___     
  \/ 3    pi
- ----- + --
    2     3
$$- \frac{\sqrt{3}}{2} + \frac{\pi}{3}$$ 
-sqrt(3)/2 + pi/3
Numerical answer [src] 
0.181172147412159
0.181172147412159

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

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