Honors AP Calculus / Mr. Hansen 2/15/2011

Name: _________________________ Bonus (for Mr. Hansen’s use only): ________

Test through Chapter 9 (Calculator Required)

Rules	You may not write calculator notation anywhere unless you cross it out. For example, fnInt(X^2,X,1,2) is not allowed; write instead. Adequate justification is required for free-response questions. All final answers in free-response portions should be circled or boxed. Decimal approximations must be correct to at least 3 places after the decimal point.
1.	Not so long ago, the centerpiece of the second semester of a standard three-semester university calculus sequence was the material in Chapter 9, techniques of integration, including trigonometric substitution. However, that is no longer true. Why not?
2.	Prove that if f is any function for which sinh^2 x is an antiderivative, then .
3.(a)	Find a 3-place decimal approximation for the area under the curve g(x) = cosh x on the interval [1.5, 3.5], and prove that this approximation is numerically equal to a 3-place approximation of the arc length over the same interval.
(b)	Prove that the equality observed in part (a) is true, in general, for any real interval [a, b]. Use reverse side if necessary.

3.	Compute Show work.
4.	Use the result of #3 to compute the exact value, if any, of Show work.
5.	Compute Show work.

6.	Compute Show work.
7.	It is possible (though not very efficient) to work #6 as a trigonometric substitution. Complete the square in the denominator to express the denominator as an expression involving “+ 16.75” and then show the reference triangle, the “LET” statement for , and the computation of in terms of dx. Do not proceed any farther.
8.	Compute Show work. Hint: Be sure to do long division first! If you need additional room, write OVER.