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GoodmanW98T2

# GoodmanW98T2 - Z 1 x 3-2 x 2 x dx 4 Evaluate each integral...

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Math 21H Feb. 19, 1998 Test #2 Name: Read each question carefully, and be sure to show clearly how you got your answers as well as what your answers are. 1. [10 points] Find Z xe - 2 x dx . 2. [10 points] Find Z sin 4 x cos 3 x dx . 3. For each of the following integrals, show what substitution or other method you would use to transform the integral into an easier integral, and show the easier integral that you get (after it is fully transformed into a different sort of integral than you started with). But to save time do not continue beyond that step. (If you try more than one method, be sure to cross out all but the one you want graded.) (a) [10 points] Z x 2 x 2 - 1 dx (b) [10 points] Z cos 2 x dx (c) [10 points]
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Unformatted text preview: Z 1 x 3-2 x 2 + x dx 4. Evaluate each integral or show that it is divergent: (a) [10 points] Z ∞ 4 1 x 3 / 2 dx . (b) [10 points] Z π sec 2 xdx . 5. [10 points] Determine whether or not this integral is convergent without evaluating it (and say how you know): Z ∞ 1 1 x + e x dx 6. [10 points] Use Simpson’s Rule to approximate Z 9 1 f ( x ) dx given the following values of f ( x ): x 1 3 5 7 9 f ( x ) 2 . 1 1 . 7 2 . 4 2 . 9 3 . 3 7. [10 points] Explain why Simpson’s Rule is a quicker way than the Trapezoidal Rule for a calculator/computer to get very accurate approximations for deﬁnite integrals....
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