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Solving integrals/ sin(x)*d(sin(x))

Integral of sin(x)*d(sin(x)) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

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

  1. The integral of a constant times a function is the constant times the integral of the function:

    1. Don't know the steps in finding this integral.

      But the integral is

    So, the result is:

  2. Now simplify:

  3. Add the constant of integration:

The answer is:

The answer (Indefinite) [src] 
  /                                              
 |                            /x   cos(x)*sin(x)\
 | sin(x)*d*sin(x) dx = C + d*|- - -------------|
 |                            \2         2      /
/
$${{d\,\left(x-{{\sin \left(2\,x\right)}\over{2}}\right)}\over{2}}$$
Simplify
The answer [src] 
  /1   cos(1)*sin(1)\
d*|- - -------------|
  \2         2      /
$$-{{\left(\sin 2-2\right)\,d}\over{4}}$$ 
=
= 
  /1   cos(1)*sin(1)\
d*|- - -------------|
  \2         2      /
$$d \left(- \frac{\sin{\left(1 \right)} \cos{\left(1 \right)}}{2} + \frac{1}{2}\right)$$
Simplify

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

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