Mister Exam

Other calculators

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
∫0π6xsin⁡2(3) dx\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:

    ∫xsin⁡2(3) dx=sin⁡2(3)∫x dx\int x \sin^{2}{\left(3 \right)}\, dx = \sin^{2}{\left(3 \right)} \int x\, dx

    1. The integral of xnx^{n} is xn+1n+1\frac{x^{n + 1}}{n + 1} when n≠−1n \neq -1:

      ∫x dx=x22\int x\, dx = \frac{x^{2}}{2}

    So, the result is: x2sin⁡2(3)2\frac{x^{2} \sin^{2}{\left(3 \right)}}{2}

  2. Add the constant of integration:

    x2sin⁡2(3)2+constant\frac{x^{2} \sin^{2}{\left(3 \right)}}{2}+ \mathrm{constant}

The answer is:

x2sin⁡2(3)2+constant\frac{x^{2} \sin^{2}{\left(3 \right)}}{2}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                             
 |                     2    2   
 |    2               x *sin (3)
 | sin (3)*x dx = C + ----------
 |                        2     
/
∫xsin⁡2(3) dx=C+x2sin⁡2(3)2\int x \sin^{2}{\left(3 \right)}\, dx = C + \frac{x^{2} \sin^{2}{\left(3 \right)}}{2}
Simplify
The graph
0.000.050.100.150.200.250.300.350.400.450.500.000.02
Plot the graph f(x)
The answer [src] 
  2    2   
pi *sin (3)
-----------
     72
π2sin⁡2(3)72\frac{\pi^{2} \sin^{2}{\left(3 \right)}}{72} 
=
= 
  2    2   
pi *sin (3)
-----------
     72
π2sin⁡2(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.

    © Mister Exam – Calculator