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
∫02ycos⁡2(x) dy\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:

    ∫ycos⁡2(x) dy=cos⁡2(x)∫y dy\int y \cos^{2}{\left(x \right)}\, dy = \cos^{2}{\left(x \right)} \int y\, dy

    1. The integral of yny^{n} is yn+1n+1\frac{y^{n + 1}}{n + 1} when n≠−1n \neq -1:

      ∫y dy=y22\int y\, dy = \frac{y^{2}}{2}

    So, the result is: y2cos⁡2(x)2\frac{y^{2} \cos^{2}{\left(x \right)}}{2}

  2. Add the constant of integration:

    y2cos⁡2(x)2+constant\frac{y^{2} \cos^{2}{\left(x \right)}}{2}+ \mathrm{constant}

The answer is:

y2cos⁡2(x)2+constant\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     
/
∫ycos⁡2(x) dy=C+y2cos⁡2(x)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)
2cos⁡2(x)2 \cos^{2}{\left(x \right)} 
=
= 
     2   
2*cos (x)
2cos⁡2(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