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‘u‘ iednesoav, Detemtie 4 mm was F'M ms: Math 129. section 07, Fali 2010 w MyAssignments Chenxing XIE‘
Math 129, section 07, Fail 201D
Homework 11 (8.1) (Homework) instructor: Lay May Yeap
@ Frill Assijlnu'lt
Question 1 2 Total
Points 5 5 10110 (100.0%)
E Description Assignment Submission in Caiculus i, we used deﬁnite integrais to ﬁnd areas, average values, and total change. We can ﬁnd
other quantities too. To do this, wedimde our quantity into smail pieces and then make an
approximation using a Riemann sum, in some cases, ail we want is the approximation lfwe want the
exact vaiue, wecompute the corresponding deﬁnite integral In this ﬁrst section we use this approach to
soive problems in geometry For this assignment, the number ofsubmissions for
each answer box is counted independentiy, The
number of submissions remaining changes oniy if you
submit a new orchanged answer, B Instructions
Each prohiem is bioken into pans to iiiustrate the connection between the Riemann sum and thedeﬁnite
integiai, You are given thevaiiable in each probiem and your work must use that variable, You shouid
aiso be able to set up and compiete a probiem by choosing your own variable Remember, your answers
should be in exact form, Write a Riemann sum and then a deﬁnite integrai representing the area of the region, using the strip shown in the ﬁgure below
where a = 3 and b = 6. Evaluate the integral exactly. Use your work to answer the questions beiow. H—b—H I
i EL *1 Himgvt
Am What is the approximate area of the strip With respect to x? (Use Deitax for Ax as necessary.)
— Ev In your deﬁnite integral what is the lower endpoint? Ii In your deﬁnite integral what is the upper endpoint? Ii What is the resuit when you evaluate the deﬁnite integral? lav What is the area of the entire triangle? I «I
symboiic loimatting heip Write a Riemann sum and then a deﬁnite integrai representing the area of the region, using the strip shown in the ﬁgure below
where a : B and b : 10. Evaiuate the integrai exactiy. use your work to answer the questions below. what is the approximate area of the strip With respect to h? (Use Deltah for Ah as necessary.)
— av In your deﬁnite integral what is the lower endpoint? It! In your deﬁnite integral what is the upper endpoint? I" What is the resuit when you evaluate the deﬁnite integral?
I " What is the area of the entire triangle? I Ev
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 Spring '08
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