2010 Calculus Probs

[sidius]

Trying to integrate this #56 from the 10B test.
Usually my TI-89 makes Calculus problems a cinch.
I can solve the problem by hand perfectly using chain rule and get the correction solution of .483
However, it seems way too time consuming for a 30 minute calc test. It seems like the TI is missing
something and just goes onto infinity.
What catch am I missing?

[AuSmith]

Looks like a regular u-substitution to me. Is that what you mean by chain rule? Let [unparseable or potentially dangerous latex formula]?

[SumitG]

I believe that the reason your 89 is having problems is because at [unparseable or potentially dangerous latex formula], the function you're integrating is undefined.

[sidius]

Well what's the catch? I assume since it's on the calculator test there has to be
a way to solve it on the calculator. Since 2005, these are the only #56 Calculus
problems the TI-89 hasn't been able to handle, and I REALLY am trying to avoid
teaching my 10th graders full-blown calculus.

[AuSmith]

Maybe you can split it into two integrals to avoid the singularity?

[calcguy]

I checked with the Calculator Applications Director and he acknowledged that the function in problem 10B-56 is not integrable. He didn't catch the mistake until after the test was given. He said for the test set sold by the UIL he will change the limits of integration from 0 → π/4 to π/8 → π/4 in order to avoid the vertical asymptote. This will make the problem workable by hand or on the TI calculator. The answer to the corrected problem is —0.240.

Also on the same test, he said the correct answer to problem 10B-47 (linear regression problem) is 1.94 (instead of 1.91).

[SumitG]

[sidius]

[calcguy]

Problem 10G-56 solved very quickly and easily on my TI-89.
Make sure that after you type in the equation and the final close parentheses, to type in "|0 < b < 0.3" (the vertical bar means "such that").

[sexyasiangirl]

also very easy to solve by hand

[sidius]

Got it. Thanks!

[sidius]

Any shortcut suggestions for chugging these out on an 89?

[SumitG]

For the first one, I would only use my calculator to find the x-intercept. First, I would see that the derivative of the function given is equal to -2Bx, and at x=-4, this is 8B=1/2, implying that B=1/16. Then, you see the y-intercept is 4, and so A=4, and your function is 4-(1/16)x^2. Set this equal to 0 and solve.

The second one I'm really not sure...seeing it on a calculator test, I would use the max and min functions on the 89 on a restricted interval, but I also wonder if you could find an expression for the amplitude on certain restricted intervals...