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Integral of 0,5*sin(x+y^2) dx

Limits of integration:

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The graph:

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Piecewise:

The solution

You have entered [src]
  1               
  /               
 |                
 |     /     2\   
 |  sin\x + y /   
 |  ----------- dx
 |       2        
 |                
/                 
0                 
$$\int\limits_{0}^{1} \frac{\sin{\left(x + y^{2} \right)}}{2}\, dx$$
Integral(sin(x + y^2)/2, (x, 0, 1))
Detail solution
  1. The integral of a constant times a function is the constant times the integral of the function:

    1. Let .

      Then let and substitute :

      1. The integral of sine is negative cosine:

      Now substitute back in:

    So, the result is:

  2. Add the constant of integration:


The answer is:

The answer (Indefinite) [src]
  /                                
 |                                 
 |    /     2\             /     2\
 | sin\x + y /          cos\x + y /
 | ----------- dx = C - -----------
 |      2                    2     
 |                                 
/                                  
$$\int \frac{\sin{\left(x + y^{2} \right)}}{2}\, dx = C - \frac{\cos{\left(x + y^{2} \right)}}{2}$$
The answer [src]
   / 2\      /     2\
cos\y /   cos\1 + y /
------- - -----------
   2           2     
$$\frac{\cos{\left(y^{2} \right)}}{2} - \frac{\cos{\left(y^{2} + 1 \right)}}{2}$$
=
=
   / 2\      /     2\
cos\y /   cos\1 + y /
------- - -----------
   2           2     
$$\frac{\cos{\left(y^{2} \right)}}{2} - \frac{\cos{\left(y^{2} + 1 \right)}}{2}$$
cos(y^2)/2 - cos(1 + y^2)/2

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