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Integral of d{x}:
Integral of sin^2t*cost
Integral of X^4*log(x)
Integral of ysinx
Integral of (x²-1)³
Identical expressions
sin^2t*cost
sinus of squared t multiply by co sinus of e of t
sin2t*cost
sin²t*cost
sin to the power of 2t*cost
sin^2tcost
sin2tcost

Solving integrals/ sin^2t*cost

Integral of sin^2t*cost dt

The solution

You have entered [src]

  1                  
  /                  
 |                   
 |     2             
 |  sin (t)*cos(t) dt
 |                   
/                    
0

$$\int\limits_{0}^{1} \sin^{2}{\left(t \right)} \cos{\left(t \right)}\, dt$$

Simplify

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

$${{\sin ^3t}\over{3}}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

   3   
sin (1)
-------
   3

$${{\sin ^31}\over{3}}$$

   3   
sin (1)
-------
   3

$$\frac{\sin^{3}{\left(1 \right)}}{3}$$

Simplify

Numerical answer [src]

0.198607745530319

0.198607745530319

The graph

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

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How to use it?

Identical expressions

Integral of sin^2t*cost dt

Limits of integration:

The graph:

Piecewise:

The solution