Unformatted text preview: Z 1 x 32 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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 Winter '98
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