Evaluate the integrals \int_0^{\pi/4}[\sec t i+\tan^2 t j-t\sin t k]dt

babeeb0oL

babeeb0oL

Answered question

2021-10-24

Evaluate the integrals
0π4[secti+tan2tjtsintk]dt

Answer & Explanation

Khribechy

Khribechy

Skilled2021-10-25Added 100 answers

To find the integral 0π4[secti+tan2tjtsintk]dt
Explanation:
0π4[secti+tan2tjtsintk]dt=[0π4sectdt]i+[0π4tan2tdt]j[0π4tsintdt]k
=I1i+I2jI3k
Where I1=0π4sectdt,I2=0π4,I=0π4sintdt
I1=0π4sectdt
On integrating
=[ln|sect+tant|]0π4
=[ln|sec(π4)+tan(π4)|ln|sec(0)+tan(0)|]
=[ln|2+1|ln|1|]
=[ln|2+1|]
I2=0π4tan2tdt
=0π4(sec2t1)dt
=

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