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Unformatted text preview: Z 1 √ x 2 + 16 dx We use the trigonometric substitution x = 4 tan θ , then dx = 4 sec 2 θdθ . Thus Z 1 √ x 2 + 16 dx = Z 4 sec 2 θ 4 sec θ dθ = Z sec θdθ = ln  sec θ + tan θ  + C = ln ± ± ± ± ± √ x 2 + 16 4 + x 4 ± ± ± ± ± + C 2. Use Simpson’s Rule to approximate Z 3 1 1 + y 5 dy for n = 6. You do not have to compute a ﬁnal numerical value. Deﬁne f ( y ) = 1 1+ y 5 and notice that Δ x = 36 = . 5. Using Simpson’s Rule we have that Z 3 1 1 + y 5 dy ≈ 1 3 1 2 [ f (0) + 4 f ( 1 2 ) + 2 f (1) + 4 f ( 3 2 ) + 2 f (2) + 4 f ( 5 2 ) + f (3)] ....
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 Spring '07
 Mikulevicius
 Math, Calculus, dx, 4 sec, Mathias Knape

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