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Solving integrals/ (sin8xcos2x)/4

Integral of (sin8xcos2x)/4 dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
 pi                     
 --                     
 61                     
  /                     
 |                      
 |  sin(8*x)*cos(2*x)   
 |  ----------------- dx
 |          4           
 |                      
/                       
0
∫0π61sin⁡(8x)cos⁡(2x)4 dx\int\limits_{0}^{\frac{\pi}{61}} \frac{\sin{\left(8 x \right)} \cos{\left(2 x \right)}}{4}\, dx 
Integral((sin(8*x)*cos(2*x))/4, (x, 0, pi/61))
The graph
0.0000.0050.0100.0150.0200.0250.0300.0350.0400.0450.0500.2-0.1
Plot the graph f(x)
The answer [src] 
        /2*pi\    /8*pi\      /2*pi\    /8*pi\
     cos|----|*cos|----|   sin|----|*sin|----|
1       \ 61 /    \ 61 /      \ 61 /    \ 61 /
-- - ------------------- - -------------------
30            30                   120
−cos⁡(2π61)cos⁡(8π61)30−sin⁡(2π61)sin⁡(8π61)120+130- \frac{\cos{\left(\frac{2 \pi}{61} \right)} \cos{\left(\frac{8 \pi}{61} \right)}}{30} - \frac{\sin{\left(\frac{2 \pi}{61} \right)} \sin{\left(\frac{8 \pi}{61} \right)}}{120} + \frac{1}{30} 
=
= 
        /2*pi\    /8*pi\      /2*pi\    /8*pi\
     cos|----|*cos|----|   sin|----|*sin|----|
1       \ 61 /    \ 61 /      \ 61 /    \ 61 /
-- - ------------------- - -------------------
30            30                   120
−cos⁡(2π61)cos⁡(8π61)30−sin⁡(2π61)sin⁡(8π61)120+130- \frac{\cos{\left(\frac{2 \pi}{61} \right)} \cos{\left(\frac{8 \pi}{61} \right)}}{30} - \frac{\sin{\left(\frac{2 \pi}{61} \right)} \sin{\left(\frac{8 \pi}{61} \right)}}{120} + \frac{1}{30} 
1/30 - cos(2*pi/61)*cos(8*pi/61)/30 - sin(2*pi/61)*sin(8*pi/61)/120
Numerical answer [src] 
0.00260819738705259
0.00260819738705259

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

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