Integral of (2sinx-cosx)dx dx

The solution

You have entered [src]

 pi                       
 --                       
 2                        
  /                       
 |                        
 |  (2*sin(x) - cos(x)) dx
 |                        
/                         
pi                        
--                        
2

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

Integral(2*sin(x) - cos(x), (x, pi/2, pi/2))

Detail solution

Integrate term-by-term:
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int 2 \sin{\left(x \right)}\, dx = 2 \int \sin{\left(x \right)}\, dx$
  1. The integral of sine is negative cosine:
    
    $\int \sin{\left(x \right)}\, dx = - \cos{\left(x \right)}$
  So, the result is: $- 2 \cos{\left(x \right)}$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \left(- \cos{\left(x \right)}\right)\, dx = - \int \cos{\left(x \right)}\, dx$
  1. The integral of cosine is sine:
    
    $\int \cos{\left(x \right)}\, dx = \sin{\left(x \right)}$
  So, the result is: $- \sin{\left(x \right)}$
The result is: $- \sin{\left(x \right)} - 2 \cos{\left(x \right)}$
Add the constant of integration:

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

The answer is:

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

The answer (Indefinite) [src]

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

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

Simplify

The graph

Plot the graph f(x)

The answer [src]

$$0$$

Numerical answer [src]

0.0

0.0

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

Other calculators

How to use it?

Identical expressions

Similar expressions

Integral of (2sinx-cosx)dx dx

Limits of integration:

The graph:

Piecewise:

The solution