Mister Exam

Integral of 2sin4x dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src]
  0              
  /              
 |               
 |  2*sin(4*x) dx
 |               
/                
pi               
--               
4                
$$\int\limits_{\frac{\pi}{4}}^{0} 2 \sin{\left(4 x \right)}\, dx$$
Integral(2*sin(4*x), (x, pi/4, 0))
Detail solution
  1. The integral of a constant times a function is the constant times the integral of the function:

    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:

    So, the result is:

  2. Add the constant of integration:


The answer is:

The answer (Indefinite) [src]
  /                            
 |                     cos(4*x)
 | 2*sin(4*x) dx = C - --------
 |                        2    
/                              
$$-{{\cos \left(4\,x\right)}\over{2}}$$
The graph
The answer [src]
-1
$$2\,\left({{\cos \pi}\over{4}}-{{1}\over{4}}\right)$$
=
=
-1
$$-1$$
Numerical answer [src]
-1.0
-1.0
The graph
Integral of 2sin4x dx

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