Mister Exam

Other calculators

Integral of (sin^4)(x)*cosx dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src]
 pi                    
 --                    
 4                     
  /                    
 |                     
 |     4               
 |  sin (x)*x*cos(x) dx
 |                     
/                      
pi                     
--                     
6                      
$$\int\limits_{\frac{\pi}{6}}^{\frac{\pi}{4}} x \sin^{4}{\left(x \right)} \cos{\left(x \right)}\, dx$$
Integral((sin(x)^4*x)*cos(x), (x, pi/6, pi/4))
The answer (Indefinite) [src]
  /                                                                                    
 |                                5           5         4                  3       2   
 |    4                      8*cos (x)   x*sin (x)   sin (x)*cos(x)   4*cos (x)*sin (x)
 | sin (x)*x*cos(x) dx = C + --------- + --------- + -------------- + -----------------
 |                               75          5             5                  15       
/                                                                                      
$$\int x \sin^{4}{\left(x \right)} \cos{\left(x \right)}\, dx = C + \frac{x \sin^{5}{\left(x \right)}}{5} + \frac{\sin^{4}{\left(x \right)} \cos{\left(x \right)}}{5} + \frac{4 \sin^{2}{\left(x \right)} \cos^{3}{\left(x \right)}}{15} + \frac{8 \cos^{5}{\left(x \right)}}{75}$$
The graph
The answer [src]
       ___              ___        ___
  49*\/ 3     pi   43*\/ 2    pi*\/ 2 
- -------- - --- + -------- + --------
    800      960     600        160   
$$- \frac{49 \sqrt{3}}{800} - \frac{\pi}{960} + \frac{\sqrt{2} \pi}{160} + \frac{43 \sqrt{2}}{600}$$
=
=
       ___              ___        ___
  49*\/ 3     pi   43*\/ 2    pi*\/ 2 
- -------- - --- + -------- + --------
    800      960     600        160   
$$- \frac{49 \sqrt{3}}{800} - \frac{\pi}{960} + \frac{\sqrt{2} \pi}{160} + \frac{43 \sqrt{2}}{600}$$
-49*sqrt(3)/800 - pi/960 + 43*sqrt(2)/600 + pi*sqrt(2)/160
Numerical answer [src]
0.0197593860224785
0.0197593860224785

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