Sheet5 - Math 21B Kouba Challenge Sheet 5 1 Use any method...

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Unformatted text preview: Math 21B Kouba Challenge Sheet 5 1.) Use any method to integrate the following. 1 1 d b. d a)/:B+1 a: )/$2+1 CC 1 1 c)/m3+1dzc d.)/$4+1dw 1 a: d f d e)/x(:c4+1) m )/x4+1 a: 1 g.)/j)—S—,E—~dm h.)/—,—da: l—smrc l—smm coszr — srnac Sing; — sm 3: 1 :I:+4 k. ———-—— l. —-———-—-——d )/w2+8x+16 dc” )/m2+8x+18 ”7" a: w+1 . ——~————d . ~———————d m) /x2+8x+20 9” n)/3x2+8a:+20 ”3 2‘) a.) Let f be a continuous function on the interval [0, a]. Show that /0af(:r) dmz/Oafla—sc) d3: ‘ 3 77/2 . sm m b.) Use part a.) to evaluate / —. 3 da: 0 Sin m + cos3 a: 3.) Inside the larger semi—circle of radius 4 is inscribed a square. Inside the square sit a smaller semi—circle and an isosceles triangle (with base parallel to the diameter of the larger semi-circle). Determine the area of the triangle. A ?1 ...
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