Solution11.pdf - HOMEWORK XI Calculus I Solution 1 Express the limit as a definite integral on the interval[2 6 lim n Solution R6 cos x x 2 n X cos x i

Solution11.pdf - HOMEWORK XI Calculus I Solution 1 Express...

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HOMEWORK XI Calculus I 1. Express the limit as a definite integral on the interval [2,6]:limnΔxi2cosxxdx 2. Use the Midpoint Rule withn= 5 to estimate the integralR20 3. Evaluate the integrals:(i).R3-2(x2-3)dx Solution : 1
HOMEWORK XI Calculus I 4. Find the general indefinite integralRsin 2xsinxdx 2
HOMEWORK XI Calculus I Solution (i). Find the displacement during the time [1,6]. Solution:Z61v(t)dt=Z61t2-2t-8dt=t33-t2-8t61=-103 (ii). Find the distance traveled by the particle during time [1,6]. Solution:v(t) =t2-2t-8 = (t+ 2)(t-4), sov(t)>0 whent <-2 ort >4,v(t)<when-2< t <4.Z61|v(t)|dt=Z41|v(t)|dt+Z64|v(t)|dt=Z41-v(t)dt+Z64v(t)dt=Z41-t2+ 2t+ 8dt+Z64t2-2t-8dt= (-t33+t2+ 8t)41+ (t33-t2-8t)64=983 3

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