M138Assign1W06wMaple

C evaluate 0 t ex sin x dx es sint s ds 0 d evaluate e

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Unformatted text preview: doing two integrations by parts. 4. Use integration by parts to prove each reduction formula. 1 n−1 cosn−1 x sin x + In−2 n n a) In = cosn x dx ⇒ In = b) In = (ln x)n dx ⇒ In = x(ln x)n − nIn−1 f (x) dx. x − 3x + 2 3. *a) Find constants A and B such that *b) Hence find the general antiderivative 1 dx sin x − 1 5. a) Find the area of the region bounded by y = 0, and y = xe−x , for 0 ≤ x ≤ b. What happens to this area as b → +∞? 1 *b) Find the area enclosed by y = ln x, y = − 1, and x = e. x 2 t metres per *6. A rocket lifts off at t = 0 and has velocity v (t) = −9.8t − 3000 ln 1 − 375 second. Find the height of the rocket 1 minute after lift off. 7. Sketch a graph of each curve, develop a definite integral representing its length (as in Example 1 on page 17 of your Course Notes), and then evaluate the integral to find the length. 1 1 a) the curve y = x3 + for 1 ≤ x ≤ 3 ; 6 2x *b) the closed curve x2/3 + y 2/3 = 1 ; 1 c) the catenary y = (ex + e−x ) for −1 ≤ x ≤ 1 . 2 d) the curve y = ln(cos x) for 0 ≤ x ≤ π/4. *8. Suppose t...
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This note was uploaded on 05/23/2010 for the course MATH 138 taught by Professor Anoymous during the Fall '07 term at Waterloo.

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