Mister Exam

Lang:

Other calculators

How to use it?
Integral of d{x}:
Integral of 2xdx
Integral of t*exp(-t)
Integral of cot^4x
Integral of x/sqrt(3x+1)
Identical expressions
dx/2cosx+3sinx
dx divide by 2 co sinus of e of x plus 3 sinus of x
dx divide by 2cosx+3sinx
Similar expressions
dx/2cosx-3sinx

Solving integrals/ dx/2cosx+3sinx

Integral of dx/2cosx+3sinx dx

The solution

You have entered [src]

  1                           
  /                           
 |                            
 |  /  1                  \   
 |  |1*-*cos(x) + 3*sin(x)| dx
 |  \  2                  /   
 |                            
/                             
0

$$\int\limits_{0}^{1} \left(3 \sin{\left(x \right)} + 1 \cdot \frac{1}{2} \cos{\left(x \right)}\right)\, dx$$

Integral(1*cos(x)/2 + 3*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:
  
  $\int 3 \sin{\left(x \right)}\, dx = 3 \int \sin{\left(x \right)}\, dx$
  1. The integral of sine is negative cosine:
    
    $\int \sin{\left(x \right)}\, dx = - \cos{\left(x \right)}$
  So, the result is: $- 3 \cos{\left(x \right)}$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int 1 \cdot \frac{1}{2} \cos{\left(x \right)}\, dx = \frac{\int \cos{\left(x \right)}\, dx}{2}$
  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: $\frac{\sin{\left(x \right)}}{2} - 3 \cos{\left(x \right)}$
Add the constant of integration:

$\frac{\sin{\left(x \right)}}{2} - 3 \cos{\left(x \right)}+ \mathrm{constant}$

The answer is:

$\frac{\sin{\left(x \right)}}{2} - 3 \cos{\left(x \right)}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                                  
 |                                                   
 | /  1                  \          sin(x)           
 | |1*-*cos(x) + 3*sin(x)| dx = C + ------ - 3*cos(x)
 | \  2                  /            2              
 |                                                   
/

$$\int \left(3 \sin{\left(x \right)} + 1 \cdot \frac{1}{2} \cos{\left(x \right)}\right)\, dx = C + \frac{\sin{\left(x \right)}}{2} - 3 \cos{\left(x \right)}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

    sin(1)           
3 + ------ - 3*cos(1)
      2

$$- 3 \cos{\left(1 \right)} + \frac{\sin{\left(1 \right)}}{2} + 3$$

    sin(1)           
3 + ------ - 3*cos(1)
      2

$$- 3 \cos{\left(1 \right)} + \frac{\sin{\left(1 \right)}}{2} + 3$$

Упростить

Numerical answer [src]

1.79982857479953

1.79982857479953

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 dx/2cosx+3sinx dx

Limits of integration:

The graph:

Piecewise:

The solution