Question

Kuis ⁽¹⁰⁵⁾
₁∫² dx/(x√(x²-1))

[a.] = π/3
[b.] = π/12
[c.] = 0
[d.] = π/6
[e.] = π/4

Answer 1

Verified answer

Jawaban:

a. π/3

Penjelasan dengan langkah-langkah:

[tex]₁∫² dx/(x√(x²-1)) \\ = ₁∫² \: \frac{1}{x \sqrt{ {x}^{2} - 1 } } dx \: (c = 1) \\ = lim _{a \: \to \: {1}^{ + } }(a∫² \frac{1}{x \sqrt{ {x}^{2} - 1} }dx ) \\ = a∫² \frac{1}{x \sqrt{ {x}^{2} - 1} }dx \\ = \int \frac{1}{x \sqrt{ {x}^{2} - {1}^{2} } } dx \\ \\ ingat \\ \int \frac{1}{ x \sqrt{ {x}^{2} - {a}^{2} } } dx \: = \frac{1}{a} \times a\sec( \frac{ |x| }{a} ) \\ \\ maka \\ \frac{1}{1} \times a\sec( \frac{ |x| }{1} ) = a\sec( |x| ) \\ = a\sec( |x| ) | {}^{2} _{a} \\ = a\sec( |2| ) - a \sec( |a| ) \\ = \frac{\pi}{3} - a \sec( |a| ) \\ = \frac{\pi}{3} [/tex]