Mister Exam

Other calculators

Solving integrals/ ycos^2x

Integral of ycos^2x dy

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  2             
  /             
 |              
 |       2      
 |  y*cos (x) dy
 |              
/               
0
$$\int\limits_{0}^{2} y \cos^{2}{\left(x \right)}\, dy$$ 
Integral(y*cos(x)^2, (y, 0, 2))
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    2   
 |      2             y *cos (x)
 | y*cos (x) dy = C + ----------
 |                        2     
/
$$\int y \cos^{2}{\left(x \right)}\, dy = C + \frac{y^{2} \cos^{2}{\left(x \right)}}{2}$$
Simplify
The answer [src] 
     2   
2*cos (x)
$$2 \cos^{2}{\left(x \right)}$$ 
=
= 
     2   
2*cos (x)
$$2 \cos^{2}{\left(x \right)}$$ 
2*cos(x)^2

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

    © Mister Exam – Calculator