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Solving integrals/ sin(4x+5)

Integral of sin(4x+5) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
 10                
  /                
 |                 
 |  sin(4*x + 5) dx
 |                 
/                  
1
$$\int\limits_{1}^{10} \sin{\left(4 x + 5 \right)}\, dx$$ 
Integral(sin(4*x + 5), (x, 1, 10))
Detail solution

  1. Let .

    Then let and substitute :

    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:

    Now substitute back in:

  2. Now simplify:

  3. Add the constant of integration:

The answer is:

The answer (Indefinite) [src] 
  /                                  
 |                       cos(4*x + 5)
 | sin(4*x + 5) dx = C - ------------
 |                            4      
/
$$\int \sin{\left(4 x + 5 \right)}\, dx = C - \frac{\cos{\left(4 x + 5 \right)}}{4}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
  cos(45)   cos(9)
- ------- + ------
     4        4
$$\frac{\cos{\left(9 \right)}}{4} - \frac{\cos{\left(45 \right)}}{4}$$ 
=
= 
  cos(45)   cos(9)
- ------- + ------
     4        4
$$\frac{\cos{\left(9 \right)}}{4} - \frac{\cos{\left(45 \right)}}{4}$$ 
-cos(45)/4 + cos(9)/4
Numerical answer [src] 
-0.359113062675602
-0.359113062675602

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

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