Mister Exam

Other calculators

Solving integrals/ 4*sinx+2*cosx

Integral of 4*sinx+2*cosx dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  E                         
  -                         
  2                         
  /                         
 |                          
 |  (4*sin(x) + 2*cos(x)) dx
 |                          
/                           
0
$$\int\limits_{0}^{\frac{e}{2}} \left(4 \sin{\left(x \right)} + 2 \cos{\left(x \right)}\right)\, dx$$ 
Integral(4*sin(x) + 2*cos(x), (x, 0, E/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 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] 
  /                                                  
 |                                                   
 | (4*sin(x) + 2*cos(x)) dx = C - 4*cos(x) + 2*sin(x)
 |                                                   
/
$$\int \left(4 \sin{\left(x \right)} + 2 \cos{\left(x \right)}\right)\, dx = C + 2 \sin{\left(x \right)} - 4 \cos{\left(x \right)}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
         /E\        /E\
4 - 4*cos|-| + 2*sin|-|
         \2/        \2/
$$- 4 \cos{\left(\frac{e}{2} \right)} + 2 \sin{\left(\frac{e}{2} \right)} + 4$$ 
=
= 
         /E\        /E\
4 - 4*cos|-| + 2*sin|-|
         \2/        \2/
$$- 4 \cos{\left(\frac{e}{2} \right)} + 2 \sin{\left(\frac{e}{2} \right)} + 4$$ 
4 - 4*cos(E/2) + 2*sin(E/2)
Numerical answer [src] 
5.11505434273624
5.11505434273624

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

    © Mister Exam – Calculator