Integrate

sqrt(1 +a^2*x^2) dx

Thanks

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- Dec 19th 2007, 05:04 AMj-lee00Integrate sqrt(1 +a^2*x^2)dx
Integrate

sqrt(1 +a^2*x^2) dx

Thanks - Dec 19th 2007, 05:28 AMcolby2152
You want to do a trig substitution so that the square root term will disappear. Have you tried subbing tangent, secant, cotangent, or cosecant in for x?

- Dec 19th 2007, 05:32 AMj-lee00
i have been trying x = a*sinh u

- Dec 19th 2007, 05:46 AMcolby2152
- Dec 19th 2007, 05:54 AMJaneBennet
- Dec 19th 2007, 07:01 AMSoroban
Hello, j-lee00!

Quote:

Integrate: .

Let:

Then: .

Substitute: .

This integral requires Integration By Parts twice, or a standard formula.

. .

Back-substitute . . .

Answer: .

- Dec 19th 2007, 07:15 AMcolby2152
J Lee,

I didn't work with the geometry, but Soroban basically completed what I started for you.

-Colby - Dec 19th 2007, 08:00 AMJaneBennet
J Lee was trying to use a sinh substitution; I think the integration is easier with this substitution.

Now you can substitute the*x*back (noting that

- Dec 19th 2007, 08:30 AMj-lee00
thanks for all your assistances