Mister Exam

Integral of xsinxydy dy

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

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

  2. Add the constant of integration:


The answer is:

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

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