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sin(x)^2*x
Solving integrals/ sin(x)^2*x

Integral of sin(x)^2*x dx

Limits of integration:

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The graph:

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Piecewise:

The solution

You have entered [src] 
  1             
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 |     2        
 |  sin (x)*x dx
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0
$$\int\limits_{0}^{1} x \sin^{2}{\left(x \right)}\, dx$$ 
Integral(sin(x)^2*x, (x, 0, 1))
The answer (Indefinite) [src] 
  /                                                                      
 |                       2       2    2       2    2                     
 |    2               sin (x)   x *cos (x)   x *sin (x)   x*cos(x)*sin(x)
 | sin (x)*x dx = C + ------- + ---------- + ---------- - ---------------
 |                       4          4            4               2       
/
$$\int x \sin^{2}{\left(x \right)}\, dx = C + \frac{x^{2} \sin^{2}{\left(x \right)}}{4} + \frac{x^{2} \cos^{2}{\left(x \right)}}{4} - \frac{x \sin{\left(x \right)} \cos{\left(x \right)}}{2} + \frac{\sin^{2}{\left(x \right)}}{4}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
   2         2                   
sin (1)   cos (1)   cos(1)*sin(1)
------- + ------- - -------------
   2         4            2
$$- \frac{\sin{\left(1 \right)} \cos{\left(1 \right)}}{2} + \frac{\cos^{2}{\left(1 \right)}}{4} + \frac{\sin^{2}{\left(1 \right)}}{2}$$ 
=
= 
   2         2                   
sin (1)   cos (1)   cos(1)*sin(1)
------- + ------- - -------------
   2         4            2
$$- \frac{\sin{\left(1 \right)} \cos{\left(1 \right)}}{2} + \frac{\cos^{2}{\left(1 \right)}}{4} + \frac{\sin^{2}{\left(1 \right)}}{2}$$ 
sin(1)^2/2 + cos(1)^2/4 - cos(1)*sin(1)/2
Numerical answer [src] 
0.199693997861972
0.199693997861972
The graph
Integral of sin(x)^2*x dx

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

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