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9th - (a R u 2 1 1 u 2 du(b R sin x 1-sin 2 x dx(c R √...

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Math 119 Recitation 9 November 16, 2006 1. Use mid-point rule to approximate 5 1 x - 1 x +1 dx with n = 4. 2. Express the limit lim n →∞ n i =1 x i sin x i Δ x on [0 , π ] as a definite integral. 3. Use formal definition of integral to evaluate 5 - 1 (1 + 3 x ) dx . 4. Prove that b a xdx = b 2 - a 2 2 . 5. Find the derivative of g ( u ) = u 0 1 x + x 2 dx . 6. Evaluate the following integrals of show that they do not exist: (a) 5 - 5 2 x 3 dx . (b) 1 0 (3 + x
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Unformatted text preview: (a) R ( u 2 + 1 + 1 u 2 ) du . (b) R sin x 1-sin 2 x dx . (c) R [ √ t (1 + t )] dt . (d) R y +5 y 7 y 3 dy . (e) R 2-1 ( x-2 | x | ) dx . (f) R 1+4 x √ 1+ x +2 x 2 dx . (g) R x ( x 2 +1) 2 dx . (h) R cos( √ t ) √ t dt . (i) R √ x sin(1 + x 3 / 2 ) dx . (j) R 7 √ 4 + 3 xdx . 1...
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