I would like to evaluate \(\displaystyle{\int_{{\pi}}^{{{3}\frac{\pi}{{2}}}}}{\frac{{{1}}}{{{1}-\phi{\sin{{2}}}\theta}}}{d}\theta\)

Leia Sullivan

Leia Sullivan

Answered question

2022-04-09

I would like to evaluate
π3π211ϕsin2θdθ

Answer & Explanation

Kapovkah7hpl

Kapovkah7hpl

Beginner2022-04-10Added 14 answers

Notice,
π3π211phosin2θdθ
=π3π211ρ2tanθ1+tan2θdθ
=π3π2sec2θ1+tan2θ2ρtanθdθ
=π3π2d(tanθρ)(tanθρ)2+(1ρ2)2
=11ρ2[tan1(tanθρ1ρ2)]π3π2
=11ρ2(π2+tan1(ρ1ρ2))

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