Evaluate the integral [/int/frac{1}{ (x^2/sqrt{x^2-16) }}dx/] using the substitution [x=4/sec/theta/].

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Mathematics

Meadow Rodriguez

1 May, 21:14

Evaluate the integral [/int/frac{1}{ (x^2/sqrt{x^2-16) }}dx/] using the substitution [x=4/sec/theta/].

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Arianna Buckley · Answer 1

Using rigorous techniques of integral calculrs to integrate the given function above, the infinite integral equivalent is square root of (x2 - 16) - 4 arc tan (square root of (x2 - 16) / 4) + C where c is the constant. substituting x equals 4 sec theta, the equivalent is square root of (16/cos^2 theta - 16) - 4 arc tan (square root of (16/cos^2 theta - 16) / 4) + C.