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one / two (cosx)-5sinx
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Similar expressions
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Integral of 1/2(cosx)-5sinx dx

The solution

You have entered [src]

  1                       
  /                       
 |                        
 |  /cos(x)           \   
 |  |------ - 5*sin(x)| dx
 |  \  2              /   
 |                        
/                         
0

$$\int\limits_{0}^{1} \left(- 5 \sin{\left(x \right)} + \frac{\cos{\left(x \right)}}{2}\right)\, dx$$

Integral(cos(x)/2 - 5*sin(x), (x, 0, 1))

Detail solution

Integrate term-by-term:
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \left(- 5 \sin{\left(x \right)}\right)\, dx = - 5 \int \sin{\left(x \right)}\, dx$
  1. The integral of sine is negative cosine:
    
    $\int \sin{\left(x \right)}\, dx = - \cos{\left(x \right)}$
  So, the result is: $5 \cos{\left(x \right)}$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \frac{\cos{\left(x \right)}}{2}\, dx = \frac{\int \cos{\left(x \right)}\, dx}{2}$
  1. The integral of cosine is sine:
    
    $\int \cos{\left(x \right)}\, dx = \sin{\left(x \right)}$
  So, the result is: $\frac{\sin{\left(x \right)}}{2}$
The result is: $\frac{\sin{\left(x \right)}}{2} + 5 \cos{\left(x \right)}$
Add the constant of integration:

$\frac{\sin{\left(x \right)}}{2} + 5 \cos{\left(x \right)}+ \mathrm{constant}$

The answer is:

$\frac{\sin{\left(x \right)}}{2} + 5 \cos{\left(x \right)}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                              
 |                                               
 | /cos(x)           \          sin(x)           
 | |------ - 5*sin(x)| dx = C + ------ + 5*cos(x)
 | \  2              /            2              
 |                                               
/

$$\int \left(- 5 \sin{\left(x \right)} + \frac{\cos{\left(x \right)}}{2}\right)\, dx = C + \frac{\sin{\left(x \right)}}{2} + 5 \cos{\left(x \right)}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

     sin(1)           
-5 + ------ + 5*cos(1)
       2

$$-5 + \frac{\sin{\left(1 \right)}}{2} + 5 \cos{\left(1 \right)}$$

     sin(1)           
-5 + ------ + 5*cos(1)
       2

$$-5 + \frac{\sin{\left(1 \right)}}{2} + 5 \cos{\left(1 \right)}$$

-5 + sin(1)/2 + 5*cos(1)

Numerical answer [src]

-1.87775297825535

-1.87775297825535

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

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Identical expressions

Similar expressions

Integral of 1/2(cosx)-5sinx dx

Limits of integration:

The graph:

Piecewise:

The solution