Integral of 7cos3x dx

The solution

You have entered [src]

 pi              
 --              
 2               
  /              
 |               
 |  7*cos(3*x) dx
 |               
/                
pi               
--               
3

$$\int\limits_{\frac{\pi}{3}}^{\frac{\pi}{2}} 7 \cos{\left(3 x \right)}\, dx$$

Integral(7*cos(3*x), (x, pi/3, pi/2))

Detail solution

The integral of a constant times a function is the constant times the integral of the function:

$\int 7 \cos{\left(3 x \right)}\, dx = 7 \int \cos{\left(3 x \right)}\, dx$
1. Let $u = 3 x$ .
  
  Then let $du = 3 dx$ and substitute $\frac{du}{3}$ :
  
  $\int \frac{\cos{\left(u \right)}}{9}\, du$
  1. The integral of a constant times a function is the constant times the integral of the function:
    
    $\int \frac{\cos{\left(u \right)}}{3}\, du = \frac{\int \cos{\left(u \right)}\, du}{3}$
    1. The integral of cosine is sine:
      
      $\int \cos{\left(u \right)}\, du = \sin{\left(u \right)}$
    So, the result is: $\frac{\sin{\left(u \right)}}{3}$
  Now substitute $u$ back in:
  
  $\frac{\sin{\left(3 x \right)}}{3}$
So, the result is: $\frac{7 \sin{\left(3 x \right)}}{3}$
Add the constant of integration:

$\frac{7 \sin{\left(3 x \right)}}{3}+ \mathrm{constant}$

The answer is:

$\frac{7 \sin{\left(3 x \right)}}{3}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                              
 |                     7*sin(3*x)
 | 7*cos(3*x) dx = C + ----------
 |                         3     
/

$$\int 7 \cos{\left(3 x \right)}\, dx = C + \frac{7 \sin{\left(3 x \right)}}{3}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

-7/3

$$- \frac{7}{3}$$

-7/3

$$- \frac{7}{3}$$

Упростить

Numerical answer [src]

-2.33333333333333

-2.33333333333333

The graph

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

Other calculators

How to use it?

Identical expressions

Similar expressions

Integral of 7cos3x dx

Limits of integration:

The graph:

Piecewise:

The solution