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Solving integrals/ x*sina+y*sinx

Integral of x*sina+y*sinx dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

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

  1. Integrate term-by-term:

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

      1. The integral of is when :

      So, the result is:

    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:

    The result is:

  2. Add the constant of integration:

The answer is:

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

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

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