Mister Exam

Other calculators

sin^8x
Solving integrals/ sin^8x

Integral of sin^8x dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1           
  /           
 |            
 |     8      
 |  sin (x) dx
 |            
/             
0
$$\int\limits_{0}^{1} \sin^{8}{\left(x \right)}\, dx$$ 
Integral(sin(x)^8, (x, 0, 1))
The graph
Plot the graph f(x)
The answer [src] 
                               3                  5                7          
 35   35*cos(1)*sin(1)   35*sin (1)*cos(1)   7*sin (1)*cos(1)   sin (1)*cos(1)
--- - ---------------- - ----------------- - ---------------- - --------------
128         128                 192                 48                8
$$- \frac{35 \sin{\left(1 \right)} \cos{\left(1 \right)}}{128} - \frac{35 \sin^{3}{\left(1 \right)} \cos{\left(1 \right)}}{192} - \frac{7 \sin^{5}{\left(1 \right)} \cos{\left(1 \right)}}{48} - \frac{\sin^{7}{\left(1 \right)} \cos{\left(1 \right)}}{8} + \frac{35}{128}$$ 
=
= 
                               3                  5                7          
 35   35*cos(1)*sin(1)   35*sin (1)*cos(1)   7*sin (1)*cos(1)   sin (1)*cos(1)
--- - ---------------- - ----------------- - ---------------- - --------------
128         128                 192                 48                8
$$- \frac{35 \sin{\left(1 \right)} \cos{\left(1 \right)}}{128} - \frac{35 \sin^{3}{\left(1 \right)} \cos{\left(1 \right)}}{192} - \frac{7 \sin^{5}{\left(1 \right)} \cos{\left(1 \right)}}{48} - \frac{\sin^{7}{\left(1 \right)} \cos{\left(1 \right)}}{8} + \frac{35}{128}$$ 
35/128 - 35*cos(1)*sin(1)/128 - 35*sin(1)^3*cos(1)/192 - 7*sin(1)^5*cos(1)/48 - sin(1)^7*cos(1)/8
Numerical answer [src] 
0.0370177996886868
0.0370177996886868
The graph
Integral of sin^8x dx

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

    © Mister Exam – Calculator