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Integral of cost*(sint)^2
Identical expressions
cost*(sint)^ two
co sinus of e of t multiply by ( sinus of t) squared
co sinus of e of t multiply by ( sinus of t) to the power of two
cost*(sint)2
cost*sint2
cost*(sint)²
cost*(sint) to the power of 2
cost(sint)^2
cost(sint)2
costsint2
costsint^2

Integral of cost*(sint)^2 dt

The solution

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 2*pi                 
   /                  
  |                   
  |            2      
  |  cos(t)*sin (t) dt
  |                   
 /                    
 0

$$\int\limits_{0}^{2 \pi} \sin^{2}{\left(t \right)} \cos{\left(t \right)}\, dt$$

Integral(cos(t)*sin(t)^2, (t, 0, 2*pi))

Detail solution

Let $u = \sin{\left(t \right)}$ .

Then let $du = \cos{\left(t \right)} dt$ and substitute $du$ :

$\int u^{2}\, du$
1. The integral of $u^{n}$ is $\frac{u^{n + 1}}{n + 1}$ when $n \neq -1$ :
  
  $\int u^{2}\, du = \frac{u^{3}}{3}$
Now substitute $u$ back in:

$\frac{\sin^{3}{\left(t \right)}}{3}$
Add the constant of integration:

$\frac{\sin^{3}{\left(t \right)}}{3}+ \mathrm{constant}$

The answer is:

$\frac{\sin^{3}{\left(t \right)}}{3}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                               
 |                            3   
 |           2             sin (t)
 | cos(t)*sin (t) dt = C + -------
 |                            3   
/

$$\int \sin^{2}{\left(t \right)} \cos{\left(t \right)}\, dt = C + \frac{\sin^{3}{\left(t \right)}}{3}$$

Simplify

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Plot the graph f(x)

The answer [src]

$$0$$

Numerical answer [src]

2.1911687993915e-22

2.1911687993915e-22

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

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Identical expressions

Integral of cost*(sint)^2 dt

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The solution