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x^2sin^2x
Solving integrals/ x^2sin^2x

Integral of x^2sin^2x dx

Limits of integration:

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The graph:

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Piecewise:

The solution

You have entered [src] 
  1              
  /              
 |               
 |   2    2      
 |  x *sin (x) dx
 |               
/                
0
$$\int\limits_{0}^{1} x^{2} \sin^{2}{\left(x \right)}\, dx$$ 
Integral(x^2*sin(x)^2, (x, 0, 1))
The answer (Indefinite) [src] 
  /                                                                                                      
 |                          2           2                       3    2       3    2       2              
 |  2    2             x*cos (x)   x*sin (x)   cos(x)*sin(x)   x *cos (x)   x *sin (x)   x *cos(x)*sin(x)
 | x *sin (x) dx = C - --------- + --------- + ------------- + ---------- + ---------- - ----------------
 |                         4           4             4             6            6               2        
/
$$\int x^{2} \sin^{2}{\left(x \right)}\, dx = C + \frac{x^{3} \sin^{2}{\left(x \right)}}{6} + \frac{x^{3} \cos^{2}{\left(x \right)}}{6} - \frac{x^{2} \sin{\left(x \right)} \cos{\left(x \right)}}{2} + \frac{x \sin^{2}{\left(x \right)}}{4} - \frac{x \cos^{2}{\left(x \right)}}{4} + \frac{\sin{\left(x \right)} \cos{\left(x \right)}}{4}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
     2           2                   
  cos (1)   5*sin (1)   cos(1)*sin(1)
- ------- + --------- - -------------
     12         12            4
$$- \frac{\sin{\left(1 \right)} \cos{\left(1 \right)}}{4} - \frac{\cos^{2}{\left(1 \right)}}{12} + \frac{5 \sin^{2}{\left(1 \right)}}{12}$$ 
=
= 
     2           2                   
  cos (1)   5*sin (1)   cos(1)*sin(1)
- ------- + --------- - -------------
     12         12            4
$$- \frac{\sin{\left(1 \right)} \cos{\left(1 \right)}}{4} - \frac{\cos^{2}{\left(1 \right)}}{12} + \frac{5 \sin^{2}{\left(1 \right)}}{12}$$ 
-cos(1)^2/12 + 5*sin(1)^2/12 - cos(1)*sin(1)/4
Numerical answer [src] 
0.157041197450242
0.157041197450242
The graph
Integral of x^2sin^2x dx

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

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