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3 years ago

Integral of cosecx dx =log|tanx/2| show that.

Mathematics

1 answer:

Pie3 years ago

7 0

ANSWER:

Let t = logtan[x/2]

⇒dt = 1/ tan[x/2] * sec² x/2 × ½ dx

⇒dt = 1/2 cos² x/2 × cot x/2dx

⇒dt = 1/2 * 1/ cos² x/2 × cosx/2 / sin x/2 dx

⇒dt = 1/2 cosx/2 / sin x/2 dx

⇒dt = 1/sinxdx

⇒dt = cosecxdx

Putting it in the integration we get,

∫cosecx / log tan(x/2)dx

= ∫dt/t

= log∣t∣+c

= log∣logtan x/2∣+c where t = logtan x/2

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Hi!

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2 years ago

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shusha [124]

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In this exercise, you're required to plot a graph for the data (velocity and time) recorded for an object that is falling from rest.

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