Integral of sinx/2cosx dx

The solution

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  1                 
  /                 
 |                  
 |  sin(x)*cos(x)   
 |  ------------- dx
 |        2         
 |                  
/                   
0

$$\int\limits_{0}^{1} \frac{\sin{\left(x \right)} \cos{\left(x \right)}}{2}\, dx$$

Integral(sin(x)*cos(x)/2, (x, 0, 1))

Detail solution

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

$\int \frac{\sin{\left(x \right)} \cos{\left(x \right)}}{2}\, dx = \frac{\int \sin{\left(x \right)} \cos{\left(x \right)}\, dx}{2}$
1. There are multiple ways to do this integral.
  Method #1
  1. Let $u = \cos{\left(x \right)}$ .
    
    Then let $du = - \sin{\left(x \right)} dx$ and substitute $- du$ :
    
    $\int u\, du$
    1. The integral of a constant times a function is the constant times the integral of the function:
      
      $\int \left(- u\right)\, du = - \int u\, du$
      
      The integral of $u^{n}$ is $\frac{u^{n + 1}}{n + 1}$ when $n \neq -1$ :
      
      $\int u\, du = \frac{u^{2}}{2}$
      
      So, the result is: $- \frac{u^{2}}{2}$
    Now substitute $u$ back in:
    
    $- \frac{\cos^{2}{\left(x \right)}}{2}$
  Method #2
  1. Let $u = \sin{\left(x \right)}$ .
    
    Then let $du = \cos{\left(x \right)} dx$ and substitute $du$ :
    
    $\int u\, du$
    1. The integral of $u^{n}$ is $\frac{u^{n + 1}}{n + 1}$ when $n \neq -1$ :
      
      $\int u\, du = \frac{u^{2}}{2}$
    Now substitute $u$ back in:
    
    $\frac{\sin^{2}{\left(x \right)}}{2}$
So, the result is: $- \frac{\cos^{2}{\left(x \right)}}{4}$
Add the constant of integration:

$- \frac{\cos^{2}{\left(x \right)}}{4}+ \mathrm{constant}$

The answer is:

$- \frac{\cos^{2}{\left(x \right)}}{4}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                              
 |                           2   
 | sin(x)*cos(x)          cos (x)
 | ------------- dx = C - -------
 |       2                   4   
 |                               
/

$$-{{\cos ^2x}\over{4}}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

   2   
sin (1)
-------
   4

$${{{{1}\over{2}}-{{\cos ^21}\over{2}}}\over{2}}$$

   2   
sin (1)
-------
   4

$$\frac{\sin^{2}{\left(1 \right)}}{4}$$

Simplify

Numerical answer [src]

0.177018354568393

0.177018354568393

The graph

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

Other calculators

How to use it?

Identical expressions

Similar expressions

Integral of sinx/2cosx dx

Limits of integration:

The graph:

Piecewise:

The solution

Method #1

Method #2