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x*sin(x²)
Solving integrals/ x*sin(x²)

Integral of x*sin(x²) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1             
  /             
 |              
 |       / 2\   
 |  x*sin\x / dx
 |              
/               
0
$$\int\limits_{0}^{1} x \sin{\left(x^{2} \right)}\, dx$$ 
Integral(x*sin(x^2), (x, 0, 1))
Detail solution

  1. Let .

    Then let and substitute :

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

      1. The integral of sine is negative cosine:

      So, the result is:

    Now substitute back in:

  2. Add the constant of integration:

The answer is:

The answer (Indefinite) [src] 
  /                          
 |                       / 2\
 |      / 2\          cos\x /
 | x*sin\x / dx = C - -------
 |                       2   
/
$$-{{\cos x^2}\over{2}}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
1   cos(1)
- - ------
2     2
$${{1}\over{2}}-{{\cos 1}\over{2}}$$ 
=
= 
1   cos(1)
- - ------
2     2
$$- \frac{\cos{\left(1 \right)}}{2} + \frac{1}{2}$$
Simplify
Numerical answer [src] 
0.22984884706593
0.22984884706593
The graph
Integral of x*sin(x²) dx

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

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