Re: Could you provide a couple examples? Message #4 Posted by Eddie Shore on 17 Oct 2004, 12:52 p.m., in response to message #3 by Ben Salinas
You are correct, the TI CAS caluclators use Derive.
Performance notes:
For TI: TI-89 Titanium using 2nd Integral command
For HP: HP-49G+ Use SYMB-CALC-INTVX command; Real Mode
1. integral((sin x)^2 * (cos x)^3) = -((sin x)^5 ÷ 5 - (sin x)^3 ÷ 3)
TI was slightly faster, but HP's answer was more simplified.
2. integral(x^2 * sqrt(x^2 + a^2))
TI returned (-a^4 * ln(sqrt(x^2+a^2)+x)÷8 + (x*(x^2+a^2)^1.5)÷4 - (a^2*x*sqrt(x^2+a^2))÷8
HP returned
Both returned the answer in the same time, with both answers several screens long.
3. integral(acos(a* x)^2)
TI returned (4*a*x*(asin(a*x))^2 + 4*(2*sqrt(1-a^2*x^2)-a*pi*x)*asin(a*x)-4*pi*sqrt(1-a^2*x^2)+a*(pi^2-8)*x)÷(4*a)
HP returned -(2*acos(x*a)÷a*sqrt(-(x^2*a^2-a))) + (acos(x*a)^2 -2)÷a *x *a
TI was slightly faster, but returned the answer in one fraction, as apposed to HP "breaking up" the fraction into a few terms. The latter I think is easier to read.
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