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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 Spring '08
 Grether
 Integrals, Limit, lim, 1 sec, dx

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