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Solving integrals/ sin^2*3x

Integral of sin^2*3x dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
 pi             
 --             
 6              
  /             
 |              
 |     2        
 |  sin (3)*x dx
 |              
/               
0
$$\int\limits_{0}^{\frac{\pi}{6}} x \sin^{2}{\left(3 \right)}\, dx$$ 
Integral(sin(3)^2*x, (x, 0, pi/6))
Detail solution

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

    1. The integral of is when :

    So, the result is:

  2. Add the constant of integration:

The answer is:

The answer (Indefinite) [src] 
  /                             
 |                     2    2   
 |    2               x *sin (3)
 | sin (3)*x dx = C + ----------
 |                        2     
/
$$\int x \sin^{2}{\left(3 \right)}\, dx = C + \frac{x^{2} \sin^{2}{\left(3 \right)}}{2}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
  2    2   
pi *sin (3)
-----------
     72
$$\frac{\pi^{2} \sin^{2}{\left(3 \right)}}{72}$$ 
=
= 
  2    2   
pi *sin (3)
-----------
     72
$$\frac{\pi^{2} \sin^{2}{\left(3 \right)}}{72}$$ 
pi^2*sin(3)^2/72
Numerical answer [src] 
0.00272988551506719
0.00272988551506719

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

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