Solve: int_0^(1/3) sec^3 (pi x)dx

miklintisyt

miklintisyt

Answered question

2022-10-25

Solve:
0 1 / 3 sec 3 ( π x ) d x

Answer & Explanation

Jovanni Salinas

Jovanni Salinas

Beginner2022-10-26Added 18 answers

It can be shown that
sec 3 θ d θ = sec θ tan θ 2 + ln | sec θ + tan θ | 2 + c .
Going back to your integral, we let θ = π x and we get
F ( x ) = sec 3 ( π x ) d x = sec ( π x ) tan ( π x ) 2 π + ln | sec ( π x ) + tan ( π x ) | 2 π + c .
Thus,
0 1 / 3 sec 3 ( π x ) d x = F ( 1 / 3 ) F ( 0 )
and we are done.

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