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ycos^2x
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Integral of ycos^2x dy

The solution

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  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

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

$\int y \cos^{2}{\left(x \right)}\, dy = \cos^{2}{\left(x \right)} \int y\, dy$
1. The integral of $y^{n}$ is $\frac{y^{n + 1}}{n + 1}$ when $n \neq -1$ :
  
  $\int y\, dy = \frac{y^{2}}{2}$
So, the result is: $\frac{y^{2} \cos^{2}{\left(x \right)}}{2}$
Add the constant of integration:

$\frac{y^{2} \cos^{2}{\left(x \right)}}{2}+ \mathrm{constant}$

The answer is:

$\frac{y^{2} \cos^{2}{\left(x \right)}}{2}+ \mathrm{constant}$

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.

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Identical expressions

Integral of ycos^2x dy

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The solution