Mister Exam

Other calculators

(sinx)^6(cosx)^2
Solving integrals/ (sinx)^6(cosx)^2

Integral of (sinx)^6(cosx)^2 dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1                   
  /                   
 |                    
 |     6       2      
 |  sin (x)*cos (x) dx
 |                    
/                     
0
$$\int\limits_{0}^{1} \sin^{6}{\left(x \right)} \cos^{2}{\left(x \right)}\, dx$$ 
Integral(sin(x)^6*cos(x)^2, (x, 0, 1))
The graph
Plot the graph f(x)
The answer [src] 
                             3                5                7          
 5    5*cos(1)*sin(1)   5*sin (1)*cos(1)   sin (1)*cos(1)   sin (1)*cos(1)
--- - --------------- - ---------------- - -------------- + --------------
128         128               192                48               8
$$- \frac{5 \sin{\left(1 \right)} \cos{\left(1 \right)}}{128} - \frac{5 \sin^{3}{\left(1 \right)} \cos{\left(1 \right)}}{192} - \frac{\sin^{5}{\left(1 \right)} \cos{\left(1 \right)}}{48} + \frac{\sin^{7}{\left(1 \right)} \cos{\left(1 \right)}}{8} + \frac{5}{128}$$ 
=
= 
                             3                5                7          
 5    5*cos(1)*sin(1)   5*sin (1)*cos(1)   sin (1)*cos(1)   sin (1)*cos(1)
--- - --------------- - ---------------- - -------------- + --------------
128         128               192                48               8
$$- \frac{5 \sin{\left(1 \right)} \cos{\left(1 \right)}}{128} - \frac{5 \sin^{3}{\left(1 \right)} \cos{\left(1 \right)}}{192} - \frac{\sin^{5}{\left(1 \right)} \cos{\left(1 \right)}}{48} + \frac{\sin^{7}{\left(1 \right)} \cos{\left(1 \right)}}{8} + \frac{5}{128}$$ 
5/128 - 5*cos(1)*sin(1)/128 - 5*sin(1)^3*cos(1)/192 - sin(1)^5*cos(1)/48 + sin(1)^7*cos(1)/8
Numerical answer [src] 
0.0283457879846044
0.0283457879846044
The graph
Integral of (sinx)^6(cosx)^2 dx

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

    © Mister Exam – Calculator