Mister exam

# Integral xsin²x dx

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from to

### The solution

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$$\int\limits_{0}^{1} x \sin^{2}{\left(x \right)}\, dx$$
Integral(x*sin(x)^2, (x, 0, 1))
The graph
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1   sin (1)   cos(1)*sin(1)
- + ------- - -------------
4      4            2      
$$- \frac{\sin{\left(1 \right)} \cos{\left(1 \right)}}{2} + \frac{\sin^{2}{\left(1 \right)}}{4} + \frac{1}{4}$$
=
=
       2
1   sin (1)   cos(1)*sin(1)
- + ------- - -------------
4      4            2      
$$- \frac{\sin{\left(1 \right)} \cos{\left(1 \right)}}{2} + \frac{\sin^{2}{\left(1 \right)}}{4} + \frac{1}{4}$$
1/4 + sin(1)^2/4 - cos(1)*sin(1)/2
0.199693997861972
0.199693997861972
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$$\int x \sin^{2}{\left(x \right)}\, dx = C + \frac{x^{2} \sin^{2}{\left(x \right)}}{4} + \frac{x^{2} \cos^{2}{\left(x \right)}}{4} - \frac{x \sin{\left(x \right)} \cos{\left(x \right)}}{2} + \frac{\sin^{2}{\left(x \right)}}{4}$$