Solve the equation: \(\displaystyle{\int_{{0}}^{{\frac{\pi}{{4}}}}}{{\sec}^{{4}}\theta}{{\tan}^{{4}}\theta}{d}\theta\)

Nathanael Hansen

Nathanael Hansen

Answered question

2022-03-20

Solve the equation:
0π4sec4θtan4θdθ

Answer & Explanation

Aidyn Wall

Aidyn Wall

Beginner2022-03-21Added 10 answers

I=0π4sec4(θ)tan4(θ)dθ
=0π4sec2(θ)(1+tan2(θ))tan4(θ)dθ
=0π4tan4(θ)d(tanθ)+0π4tan6(θ)d(tanθ)
=[15tan5(θ)]0π4+[17tan7(θ)]0π4
=15+17=1235
German Ferguson

German Ferguson

Beginner2022-03-22Added 18 answers

sec4θ=(1+tan2θ)sec2θ, then substitute u=tanθ to get:
I=01(u6+u4)du
=u77+u5501
=1235

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