A TI-89/92+ Software Bug
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A TI-89/92+ Software Bug
A TI-89/92+ Software Bug
In AUTO mode The TI-89/92+ gives an output of
2*(7*x+4)*sqrt(7*x+4)^3)/5
for the input of Integral(sqrt(7*x+4)^3),x). The correct result should
be
2*(7*x+4)*sqrt(7*x+4)^3)/35. This is not an isolated problem but is a
problem for the
family of functions: Integral(sqrt(a*x+b)^n),x). That is to say the
TI-89/92+ produces wrong
results for varying values of a,b, and n. For
Integral(sqrt(2*x-3)^7),x) the TI-89/92+
produces 2*(2*x-3)*sqrt((2x-3)^7)/9 when correct result should be
(2*x-3)*sqrt((2*x-3)^7)/9.
It is interesting to note that the for Integral(sqrt(a*x+b)^n),x) the
TI-89/92+’s produce the
correct result of 2*(a*x+b)^(n/2+1)/(a*(n+2)). In APPROX mode the
TI-89/92+ gives the
correct results for the above examples.
For definite integrals problems exist also. In AUTO mode The TI-89/92+
one gets:
Integral(sqrt(7*x+4)^3),x,2,9) = 8978*sqrt(67)/5-19448sqt(2)/5 but one
should get:
8978*sqrt(67)/35-19448sqt(2)/35. In APPROX mode one gets
Integral(sqrt(7*x+4)^3),x,2,9)=2021.11 which is correct.
It should be noted that in AUTO mode when one rewrites the integrals in
exponential
form the correct results occur. For Integral((7*x+4)^(3/2),x) one gets
2*(7*x+4)^(5/2)/35
and for Integral((7*x+4)^(3/2),x,2,9) one gets
8978*sqrt(67)/35-19448sqt(2)/35.
Similar problems exist for the procedure deSolve.
Gary Wardall
UWGB math. dept
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