Integral of 2sinxcosx dx

You have entered [src]

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

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

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

Detail solution

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

$\sin^{2}{\left(x \right)}+ \mathrm{constant}$

The answer is:

$\sin^{2}{\left(x \right)}+ \mathrm{constant}$

The answer (Indefinite) [src]

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

$$\int 2 \sin{\left(x \right)} \cos{\left(x \right)}\, dx = C + \sin^{2}{\left(x \right)}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

   2   
sin (1)

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

   2   
sin (1)

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

sin(1)^2

Numerical answer [src]

0.708073418273571

0.708073418273571

The graph

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

Method #1