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dx/2sinx+3cosx
Solving integrals/ dx/2sinx+3cosx

Integral of dx/2sinx+3cosx dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1                           
  /                           
 |                            
 |  /  1                  \   
 |  |1*-*sin(x) + 3*cos(x)| dx
 |  \  2                  /   
 |                            
/                             
0
$$\int\limits_{0}^{1} \left(1 \cdot \frac{1}{2} \sin{\left(x \right)} + 3 \cos{\left(x \right)}\right)\, dx$$
Simplify
Detail solution

  1. Integrate term-by-term:

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

      1. The integral of sine is negative cosine:

      So, the result is:

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

      1. The integral of cosine is sine:

      So, the result is:

    The result is:

  2. Add the constant of integration:

The answer is:

The answer (Indefinite) [src] 
  /                                                  
 |                                                   
 | /  1                  \                     cos(x)
 | |1*-*sin(x) + 3*cos(x)| dx = C + 3*sin(x) - ------
 | \  2                  /                       2   
 |                                                   
/
$$3\,\sin x-{{\cos x}\over{2}}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
1              cos(1)
- + 3*sin(1) - ------
2                2
$${{6\,\sin 1-\cos 1+1}\over{2}}$$ 
=
= 
1              cos(1)
- + 3*sin(1) - ------
2                2
$$- \frac{\cos{\left(1 \right)}}{2} + \frac{1}{2} + 3 \sin{\left(1 \right)}$$
Simplify
Numerical answer [src] 
2.75426180148962
2.75426180148962
The graph
Integral of dx/2sinx+3cosx dx

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

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