Evaluate the integrals. \int_\sqrt{2}^2\frac{dx}{x\sqrt{x^2-1}}

Nann

Nann

Answered question

2021-10-10

Evaluate the integrals.
22dxxx21

Answer & Explanation

Brighton

Brighton

Skilled2021-10-11Added 103 answers

Evaluate,
22dxxx21
Simplification:
Since we have,
22dxxx21
Substitute
x21=u2x2x21dx=du1x21dx=1xdu
When x=2,u=1
When x=2,u=3
In (1),
22dxxx21=13dux2
=13dux2
=13du1+u2
=[tan1u]13
=[tan13tan11]
=[π3π4]
=[4π3π12]
=π12
Hence
22dxxx21=π12

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