Mister Exam

Other calculators

Solving integrals/ 2(cos^2)*sinz

Integral of 2(cos^2)*sinz dz

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
 pi                    
  /                    
 |                     
 |       2             
 |  2*cos (x)*sin(z) dz
 |                     
/                      
0
∫0πsin⁡(z)2cos⁡2(x) dz\int\limits_{0}^{\pi} \sin{\left(z \right)} 2 \cos^{2}{\left(x \right)}\, dz 
Integral((2*cos(x)^2)*sin(z), (z, 0, pi))
Detail solution

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

    ∫sin⁡(z)2cos⁡2(x) dz=2cos⁡2(x)∫sin⁡(z) dz\int \sin{\left(z \right)} 2 \cos^{2}{\left(x \right)}\, dz = 2 \cos^{2}{\left(x \right)} \int \sin{\left(z \right)}\, dz

    1. The integral of sine is negative cosine:

      ∫sin⁡(z) dz=−cos⁡(z)\int \sin{\left(z \right)}\, dz = - \cos{\left(z \right)}

    So, the result is: −2cos⁡2(x)cos⁡(z)- 2 \cos^{2}{\left(x \right)} \cos{\left(z \right)}

  2. Add the constant of integration:

    −2cos⁡2(x)cos⁡(z)+constant- 2 \cos^{2}{\left(x \right)} \cos{\left(z \right)}+ \mathrm{constant}

The answer is:

−2cos⁡2(x)cos⁡(z)+constant- 2 \cos^{2}{\left(x \right)} \cos{\left(z \right)}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                                          
 |                                           
 |      2                         2          
 | 2*cos (x)*sin(z) dz = C - 2*cos (x)*cos(z)
 |                                           
/
∫sin⁡(z)2cos⁡2(x) dz=C−2cos⁡2(x)cos⁡(z)\int \sin{\left(z \right)} 2 \cos^{2}{\left(x \right)}\, dz = C - 2 \cos^{2}{\left(x \right)} \cos{\left(z \right)}
Simplify
The answer [src] 
     2   
4*cos (x)
4cos⁡2(x)4 \cos^{2}{\left(x \right)} 
=
= 
     2   
4*cos (x)
4cos⁡2(x)4 \cos^{2}{\left(x \right)} 
4*cos(x)^2

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

    © Mister Exam – Calculator