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

Integral of 2*y*sin((y^2)/2) dy

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
   ____              
 \/ pi               
    /                
   |                 
   |          / 2\   
   |          |y |   
   |   2*y*sin|--| dy
   |          \2 /   
   |                 
  /                  
  0
$$\int\limits_{0}^{\sqrt{\pi}} 2 y \sin{\left(\frac{y^{2}}{2} \right)}\, dy$$ 
Integral((2*y)*sin(y^2/2), (y, 0, sqrt(pi)))
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. Now simplify:

  3. Add the constant of integration:

The answer is:

The answer (Indefinite) [src] 
  /                              
 |                               
 |        / 2\               / 2\
 |        |y |               |y |
 | 2*y*sin|--| dy = C - 2*cos|--|
 |        \2 /               \2 /
 |                               
/
$$\int 2 y \sin{\left(\frac{y^{2}}{2} \right)}\, dy = C - 2 \cos{\left(\frac{y^{2}}{2} \right)}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
2
$$2$$ 
=
= 
2
$$2$$ 
2
Numerical answer [src] 
2.0
2.0

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

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