Math 125 HW Ie http://www.webassign.net!web/student! Assignment -Responses/JasPd... WebAssign Math 125 HW_1C (Homework) Current Score: - / 80 Due: Wednesday, April 9 2014 11:00 PM PDT Donald Marshall Math 125 Spring 2014, section A, Spring 2014 Instructor: Donald Marshall 1. -/5 points SCalcET75.2.003.MI. If f(x) = ex - 7, 0 ~ x ~ 2, find the Riemann sum with n = 4 correct to six decimal places, taking the sample points to be midpoints. M4 = I I 2. -/6 points SCalcET7 5.2.004. (a) Find the Riemann sum for f(x) = 6 sin x, 0 ~ x ~ 31[/2, with six terms, tak ing t he sample points to be right endpoints. (Round your answers to six decimal places.) R6 = I I (b) Repeat part (a) with midpoints as the sample points. M6 = I I 3. -/6 points SCalcET75.2.007. A table of values of an increasing function f is shown. Use the table to find lower and upper 130 estimates for f(x) dx. 10 lower estimate upper estimate x 10 14 18 22 26 30 f(x) -13-6 -3 1 3 8 I of 10 4/3/20 14 10:57 AM
........ _................ _..... A... _... _................. _.............. Math 125 HW Ie http://www. webass ign.netjweb/studentj Assignment-Responses/last?d......w.................... r 4. -/5 points SCalcET7 5.2.009. Use the Midpoint Rule with the given value of n to approximate the integral. Round the answer to four decimal places. 180 sin h dx, n = 4,---------=--=,1 5. -/5 points SCalcET75.2.017.MI. Express the limit as a definite integral on the given interval. n lim ~ x. In(2 + x. 2 ) /)"x, [2, 4] n---'> oo ~ I i = 1 I dx 2 of 10 4/3/2014 10:57 AM
Math 125 HW Ie http://www.webassign.net/web/student/ Ass ignment4 Responses/Jast?d... 6. -/9 points SCalcET7 5.2.034. MI. The graph of 9 consists of two straight lines and a semicircle. Use it to evaluate each integral. y r\ - 10 \ --20 0 1\ \ r\ "-i'... y = g(x) / 20 35 J -"V I x (a) f lo Jo g(x) dx (b) 130 g(x) dx 10 (c) f 35 Jo g(x) dx 3 of 10 4/3/2014 10:57 AM
Math [25 HW 1 C http://www.webassign.net!web/student! Assignment-Responses/last?d... 7. -/5 points SCalcET7 5.2.040. Evaluate the integral by interpreting it in terms of areas. 18 o Ix - 91 dx 8. -/5 points SCalcET7 5.2.048. MI. If [5 f(x) dx = 14 and r5f(x) dx = 3.2, find [4 f(x) dx. J4. 1 1 4 of 10 4/3/2014 10:57 AM
Math 125 HW Ie http ://www.webassign.net!web/student! Ass ignment -Responses/last?d... 9. -/6 points SCalcETl 5.2.054. Suppose f has absolute minimum value m and absolute maximum value M. Between what two 8 values must 1f(x) dx lie? (smaller value) (larger value) Which property of integrals allows you to make your conclusion? If f(x) ~ 0 for a ~ x ~ b, then [b f(x) dx ~ o. I b l c o f(x) dx + f(x) dx = f(x) dx a.c a l'b If m ~ f(x) ~ M for a ~ x ~ b, then m(b - a) ~ f(x) dx ~ M(b - a). Ib a f(x) dx = 0 [ ~ a l -La b f(x) dx = f(x) dx 5 of 10 4/3/2014 10:57 AM
http://www.webassign.net/web/student/ Ass ignment -Responses/last?d... 10.-/6 points SCa lcet7 5.2.061. If m :-:; f(x) :-:; M for a :-:; x :-:; b, where m is the absolute minimum and M is the absolute maximum of f on the interval [a, b], then (b m(b - a) :-:; Ja f(x) dx :-:; M(b - a). Use this property to estimate the value of the integral. l Tr/6 Tr/8 5 tan 2x dx (smaller value) (larger value) 6 of 10 4/3/2 014 10:57 AM
Math 125 HW 1e http://www.webassign.netiweb/studenti Assignment -Responses/Jast?d... 11.-/12 points The equation x 2 l + = 1 16 9 defines an ellipse, which is graphed above. In this excercise we will approximate the area of this ellipse. (a) To get the total area of the ellipse, we could first find the area of the part of the ellipse lying in the First Quadrant, and then multiply by what factor? I I (b) Find the function y=f(x) that gives the curve bounding the top of the ellipse. (c) Use.1x= 1 and midpoints to approximate the area of the part of the ellipse lying in the First Quadrant. I I Cd) Approximate the total area of the ellipse. I '----------' 7 of 10 4/3/2014 10:57 AM
Math 125 HW Ie http://www.webassign.net/web/studenti Ass ignment -Responses/last?d... 12.-/10 points. or th following pro lem, the units of ria I re gl n along wi h th uni s for a fun tiod ( r tw fun tion.s). l ive 'he units of arh d wit in gral (a) If is in 'c nd. and I(x) is in ~ t/ro.ond ' t h n1"i( ) d:r In t t fc t,.i I b) If t is in lis ond d get } is in fe t/ onds 2 then [ ' g(t) dt i..., in tis 2 fe t/. t c ct 1" (c)ifx' in ~da; '. andf(x), it "tlearc b F" then f(~'}d:r ISm da's (g F}/day dcgr F (d gr F),da ' 8 of 10 4/3/2014 10:57 AM
Math 125 HW Ie http://www.webassign.netlw eb/studen t!ass ignm ent -Responses/last?d... (d) If X is in 'hours and 9(x) is in 'kil watts' lit n.f"9(x) dx in 1il wa t hour k.ilowa /llour kil wa how c) If L' in In crs 1 and f (L) IS ill squa.r In t.er l) hen.tj(l)dl is in m or m ersm lim ers f) If t is in minu 'I g(t)' in gallons/fo," and (t) is in fc /minu ' b n 1 9(t) (t)dt is in gallons gallons/mlnut (gallons minutes )/foot galla.f, )/minu e (g) If 's in ' onds andj )i in '~e /""c nd' hen f.' U s) 'd ill 2/ e 2 9 of 10 4/3/201410:57 AM
Math 125 HW Ie http://www.webassign.netlweb/studen tiassignment -Responses/last?d... feet c 1/1 1 (h) If. IS ill "da; and J(x) is in 'pounds then (I f(x) d.r is in I/pound: _ pound " da r /p und p und da; (i) If in "in h," Ji.). in "squar in h,. and d(.) is in p und per u i. inch' t h n [ ' A(x)d(. oj dx is in P un I'n h 8 2 P und lin hes:? p un slin h unds (j) If :1' is in 'da;vs' nd 1 ~')' in fl u Me p r day' h n ( U 1(1') dx i in Jo ~ (Bu )/d flu cas (fl u as ) da ~ ' da I flu asc) 10 of 10 4/3/2014 10:57 AM