Mister Exam

Other calculators

sin(sinx)cosx
Solving integrals/ sin(sinx)cosx

Integral of sin(sinx)cosx dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1                      
  /                      
 |                       
 |  sin(sin(x))*cos(x) dx
 |                       
/                        
0
∫01sin⁡(sin⁡(x))cos⁡(x) dx\int\limits_{0}^{1} \sin{\left(\sin{\left(x \right)} \right)} \cos{\left(x \right)}\, dx 
Integral(sin(sin(x))*cos(x), (x, 0, 1))
Detail solution

  1. Let u=sin⁡(x)u = \sin{\left(x \right)}.

    Then let du=cos⁡(x)dxdu = \cos{\left(x \right)} dx and substitute dudu:

    ∫sin⁡(u) du\int \sin{\left(u \right)}\, du

    1. The integral of sine is negative cosine:

      ∫sin⁡(u) du=−cos⁡(u)\int \sin{\left(u \right)}\, du = - \cos{\left(u \right)}

    Now substitute uu back in:

    −cos⁡(sin⁡(x))- \cos{\left(\sin{\left(x \right)} \right)}

  2. Add the constant of integration:

    −cos⁡(sin⁡(x))+constant- \cos{\left(\sin{\left(x \right)} \right)}+ \mathrm{constant}

The answer is:

−cos⁡(sin⁡(x))+constant- \cos{\left(\sin{\left(x \right)} \right)}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                                       
 |                                        
 | sin(sin(x))*cos(x) dx = C - cos(sin(x))
 |                                        
/
∫sin⁡(sin⁡(x))cos⁡(x) dx=C−cos⁡(sin⁡(x))\int \sin{\left(\sin{\left(x \right)} \right)} \cos{\left(x \right)}\, dx = C - \cos{\left(\sin{\left(x \right)} \right)}
Simplify
The graph
0.001.000.100.200.300.400.500.600.700.800.902-2
Plot the graph f(x)
The answer [src] 
1 - cos(sin(1))
1−cos⁡(sin⁡(1))1 - \cos{\left(\sin{\left(1 \right)} \right)} 
=
= 
1 - cos(sin(1))
1−cos⁡(sin⁡(1))1 - \cos{\left(\sin{\left(1 \right)} \right)} 
1 - cos(sin(1))
Numerical answer [src] 
0.333633254607119
0.333633254607119
The graph
Integral of sin(sinx)cosx dx

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

    © Mister Exam – Calculator