Mister Exam

Other calculators

sin(5-3x)
Solving integrals/ sin(5-3x)

Integral of sin(5-3x) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1                
  /                
 |                 
 |  sin(5 - 3*x) dx
 |                 
/                  
0
$$\int\limits_{0}^{1} \sin{\left(5 - 3 x \right)}\, dx$$ 
Integral(sin(5 - 3*x), (x, 0, 1))
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. Add the constant of integration:

The answer is:

The answer (Indefinite) [src] 
  /                                   
 |                       cos(-5 + 3*x)
 | sin(5 - 3*x) dx = C + -------------
 |                             3      
/
$$\int \sin{\left(5 - 3 x \right)}\, dx = C + \frac{\cos{\left(3 x - 5 \right)}}{3}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
  cos(5)   cos(2)
- ------ + ------
    3        3
$$\frac{\cos{\left(2 \right)}}{3} - \frac{\cos{\left(5 \right)}}{3}$$ 
=
= 
  cos(5)   cos(2)
- ------ + ------
    3        3
$$\frac{\cos{\left(2 \right)}}{3} - \frac{\cos{\left(5 \right)}}{3}$$ 
-cos(5)/3 + cos(2)/3
Numerical answer [src] 
-0.233269674003456
-0.233269674003456
The graph
Integral of sin(5-3x) dx

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

    © Mister Exam – Calculator