Asked by Katie

Find x and dx using trigonometric substitution of

(integral) square root of 4x^2 - 9 divide by x

x = 2/3 sec x
dx = 2/3 tan x dx

Is this right so far?

Answers

Answered by Steve
∫√(4x^2-9) dx

2x = 3secθ, so
4x^2-9 = 9sec^2θ-9 = 9tan^2θ
x = 2/3 secθ, so
dx = 2/3 secθ tanθ

and you integral becomes

∫3tanθ (2/3 secθ tanθ) dθ
= 2∫secθ tan^2θ dθ
= 2∫(sec^3θ - secθ) dθ

use integration by parts twice for sec^3θ.
Answered by Steve
rats. x = 3/2 secθ, so adjust the constant in the following steps.

when you're all done, you can check your answer by typing in the integral at wolframalpha.com
Answered by Katie
ok thank you very much. Happy New Year

Related Questions