Mister Exam

Integral of dx/2sinxcosx dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src]
 pi                     
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 |  0.5*sin(x)*cos(x) dx
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pi                      
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$$\int\limits_{\frac{\pi}{6}}^{\frac{\pi}{3}} 0.5 \sin{\left(x \right)} \cos{\left(x \right)}\, dx$$
Integral((0.5*sin(x))*cos(x), (x, pi/6, pi/3))
Detail solution
  1. There are multiple ways to do this integral.

    Method #1

    1. Let .

      Then let and substitute :

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

        1. The integral of is when :

        So, the result is:

      Now substitute back in:

    Method #2

    1. Let .

      Then let and substitute :

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

        1. The integral of is when :

        So, the result is:

      Now substitute back in:

  2. Add the constant of integration:


The answer is:

The answer (Indefinite) [src]
  /                                       
 |                                    2   
 | 0.5*sin(x)*cos(x) dx = C + 0.25*sin (x)
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$$\int 0.5 \sin{\left(x \right)} \cos{\left(x \right)}\, dx = C + 0.25 \sin^{2}{\left(x \right)}$$
The graph
The answer [src]
0.125000000000000
$$0.125$$
=
=
0.125000000000000
$$0.125$$
0.125000000000000
Numerical answer [src]
0.125
0.125

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