pandaxo18 pandaxo18
  • 07-11-2018
  • Mathematics
contestada

how to integrate this

how to integrate this class=

Respuesta :

TheAakash
TheAakash TheAakash
  • 07-11-2018

To integrate, let's first clean out the inside, and simplify:

[tex]16\int {(sin x)^4} \ dx[/tex]

We can now safely substitute the value of u:

[tex]u = sin x[/tex]

[tex]du = cos (x) dx[/tex]

Now, we can write that:

[tex]16\int{u^4} \ du[/tex]

This is much easier to integrate:

[tex]16\int{u^4} \ du = 16[\frac{1}{5}u^5] + C[/tex]

Simplify:

[tex]\frac{16}{5}u^5 + C[/tex]

Replace u (final answer):

[tex]\frac{16}{5}sin^5x +C[/tex]

Hope I could help with your integration.

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