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spicytaco

Member

Registered: 2009-01-23

Posts: 2

Trig Substitution Integral Help x_x

Can someone help me find the integral of 1/(4-x^2) using trig substitution? I got to (1/2)[ln sec theta + tan theta +c] but I'm pretty sure that's not the final answer.

Also what would you do to evaluate the integral from 0 to 1?

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: Trig Substitution Integral Help x_x

I'd say that's about as simple as it's going to get. Maybe turn it into (1+sinθ)/cosθ, but that's not really a simplification.

You might need to get the expression back in terms of x rather than θ, if the question wants it.
To do that, use cosθ = √(1-sin²θ) to express everything in terms of sinθ and then substitute back. (Assuming you used x = 2sinθ. There might be other substitutions that work too)

To integrate from 0 to 1, just evaluate the expression when x = 0, and take that result away from its value at x = 1.

If you're not required to get the expression in terms of x, you can take a shortcut by evaluating between θ = 0 and θ = π/4.

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