Mister Exam

Other calculators

Solving integrals/ (cosx+2sinx)

Integral of (cosx+2sinx) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  p                       
  -                       
  2                       
  /                       
 |                        
 |  (cos(x) + 2*sin(x)) dx
 |                        
/                         
0
$$\int\limits_{0}^{\frac{p}{2}} \left(2 \sin{\left(x \right)} + \cos{\left(x \right)}\right)\, dx$$ 
Integral(cos(x) + 2*sin(x), (x, 0, p/2))
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 cosine is sine:

    The result is:

  2. Add the constant of integration:

The answer is:

The answer (Indefinite) [src] 
  /                                              
 |                                               
 | (cos(x) + 2*sin(x)) dx = C - 2*cos(x) + sin(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 answer [src] 
         /p\      /p\
2 - 2*cos|-| + sin|-|
         \2/      \2/
$$\sin{\left(\frac{p}{2} \right)} - 2 \cos{\left(\frac{p}{2} \right)} + 2$$ 
=
= 
         /p\      /p\
2 - 2*cos|-| + sin|-|
         \2/      \2/
$$\sin{\left(\frac{p}{2} \right)} - 2 \cos{\left(\frac{p}{2} \right)} + 2$$ 
2 - 2*cos(p/2) + sin(p/2)

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

    © Mister Exam – Calculator