Need Help? Need Help? WebAssign Math 125 HW_1C (Homework) If f(x) = ex -

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1 Math 125 HW Ie Assignment -Responses/JasPd... WebAssign Math 125 HW_1C (Homework) Current Score: - / 80 Due: Wednesday, April :00 PM PDT Donald Marshall Math 125 Spring 2014, section A, Spring 2014 Instructor: Donald Marshall 1. -/5 points SCalcET 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 SCalcET (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 SCalcET 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 f(x) I of 10 4/3/ :57 AM

2 _ _..... A... _... _ _ Math 125 HW Ie webass ign.netjweb/studentj Assignment-Responses/last?d......w r 4. -/5 points SCalcET 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 SCalcET 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/ :57 AM

3 Math 125 HW Ie Ass ignment4 Responses/Jast?d /9 points SCalcET MI. The graph of 9 consists of two straight lines and a semicircle. Use it to evaluate each integral. y r\ - 10 \ \ \ r\ "-i'... y = g(x) / 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/ :57 AM

4 Math [25 HW 1 C Assignment-Responses/last?d /5 points SCalcET Evaluate the integral by interpreting it in terms of areas. 18 o Ix - 91 dx 8. -/5 points SCalcET MI. If [5 f(x) dx = 14 and r5f(x) dx = 3.2, find [4 f(x) dx. J of 10 4/3/ :57 AM

5 Math 125 HW Ie http :// Ass ignment -Responses/last?d /6 points SCalcETl 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/ :57 AM

6 Ass ignment -Responses/last?d /6 points SCa lcet 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/ :57 AM

7 Math 125 HW 1e Assignment -Responses/Jast?d /12 points The equation x 2 l + = 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/ :57 AM

8 Math 125 HW Ie Ass ignment -Responses/last?d /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/ :57 AM

9 Math 125 HW Ie 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

10 Math 125 HW Ie 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/ :57 AM

MATH 1242 FINAL EXAM Spring,

MATH 1242 FINAL EXAM Spring, MATH 242 FINAL EXAM Spring, 200 Part I (MULTIPLE CHOICE, NO CALCULATORS).. Find 2 4x3 dx. (a) 28 (b) 5 (c) 0 (d) 36 (e) 7 2. Find 2 cos t dt. (a) 2 sin t + C (b) 2 sin t + C (c) 2 cos t + C (d) 2 cos t