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ws33 - WORKSHEET Fall 1995 1 Write down the definition of...

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Unformatted text preview: WORKSHEET - Fall 1995 1. Write down the definition of a definite integral. Take turns explaining the different parts to the members of your group. 2. Use the definition of the definite integral to compute the following integrals: 5 1 n 3x2 − 14x + 11 n 2 0 7x. Hint: i=1 i= n(n + 1) 2 and i=1 i2 = n(n + 1)(2n + 1) 6 . 3. Find the following limits: n n→0 lim i=1 π π sin i n n n n→0 lim 2 i=1 42 i n2 Can you evaluate the second one in another way? a third? 4. Compute the following: a) d) cos x dx √ 1 + sin x 1 x dx √ 8x2 + 1 0 b) 1 cos x dx 1 + sin2 x dx 3x2 + 1 c) f) x3 sin x dx 1 −2 e) 0 dx x2 5. A man walks into a bar and after a few drinks has the following conversation with the batender: Man: Bartender: Man: Bartender: Man: Bartender: Man: Try to guess the ages of my three daughters. Well, I won’t guess but if you give me clues, I’ll try to figure it out. Ok. The sum of their ages is eighteen. That’s not enough. I need more information. Well, the age of one of them is the address above the door outside. (after returning from looking at the door) That helps, but I still don’t know all of their ages. Alright then, my youngest girl’s favorite flavor of ice cream is strawberry. At this point the bartender promptly told the man the ages of all three of his daughters. What were they? 6. Compute the following: a) d) 0 sin(ln x) dx x π /2 √ 1 + sin x cos x dx b) e) 1 ex sec2 (ex ) dx 4 c) f) 0 sin−1 x dx 1 sec−1 √ x dx ln(x + 1) dx ...
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