Mister Exam

Lang:

Integral of cos(15*x) dx

You have entered [src]

  1             
  /             
 |              
 |  cos(15*x) dx
 |              
/               
0

$$\int\limits_{0}^{1} \cos{\left(15 x \right)}\, dx$$

Integral(cos(15*x), (x, 0, 1))

Detail solution

Let $u = 15 x$ .

Then let $du = 15 dx$ and substitute $\frac{du}{15}$ :

$\int \frac{\cos{\left(u \right)}}{15}\, du$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \cos{\left(u \right)}\, du = \frac{\int \cos{\left(u \right)}\, du}{15}$
  1. The integral of cosine is sine:
    
    $\int \cos{\left(u \right)}\, du = \sin{\left(u \right)}$
  So, the result is: $\frac{\sin{\left(u \right)}}{15}$
Now substitute $u$ back in:

$\frac{\sin{\left(15 x \right)}}{15}$
Add the constant of integration:

$\frac{\sin{\left(15 x \right)}}{15}+ \mathrm{constant}$

The answer is:

$\frac{\sin{\left(15 x \right)}}{15}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                            
 |                    sin(15*x)
 | cos(15*x) dx = C + ---------
 |                        15   
/

$$\int \cos{\left(15 x \right)}\, dx = C + \frac{\sin{\left(15 x \right)}}{15}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

sin(15)
-------
   15

$$\frac{\sin{\left(15 \right)}}{15}$$

sin(15)
-------
   15

$$\frac{\sin{\left(15 \right)}}{15}$$

sin(15)/15

Numerical answer [src]

0.0433525226771411

0.0433525226771411

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