

Last updated at Dec. 8, 2016 by Teachoo
Transcript
Ex 7.6, 9 𝑥 c𝑜 𝑠−1𝑥 𝑥 cos−1𝑥 𝑑𝑥 Let x = cos𝜃 dx = − sin𝜃 𝑑𝜃 𝑥 cos−1𝑥 𝑑𝑥 = cos𝜃 𝒄𝒐𝒔−𝟏( 𝒄𝒐𝒔𝜽)(− sin𝜃 )𝑑𝜃 = sin𝜃 𝜽 cos𝜃𝑑𝜃 = −12 𝜃 (2sin𝜃 cos𝜃) 𝑑𝜃 = −12 𝜃 sin2𝜃𝑑𝜃 = −12 𝜃∫ sin2𝜃𝑑𝜃−∫ 𝑑𝜃𝑑𝜃∫sin 2𝜃 𝑑𝜃𝑑𝜃 = −12 𝜃 −( cos2𝜃)2−∫1. − (cos2𝜃)2𝑑𝜃 = −12 −𝜃2 cos2𝜃+ 12∫cos 2𝜃 𝑑𝜃 = −12 −𝜃2 cos2𝜃+ 12 sin2𝜃2 + C = 𝜃4 𝒄𝒐𝒔𝟐𝜽 – 18 𝒔𝒊𝒏𝟐𝜽 + C = 𝜃4 ( 𝟐𝒄𝒐𝒔𝟐𝜽 – 1) – 18 × 2 𝒔𝒊𝒏𝜽 𝐜𝐨𝐬 𝜽 + C = 𝜃4 ( 2𝑐𝑜𝑠2𝜃 – 1) – 14 𝑠𝑖𝑛𝜃 𝑐𝑜𝑠 𝜃 + C = 𝜃4 ( 2𝑐𝑜𝑠2𝜃 – 1) – 14 𝑐𝑜𝑠𝜃 1− cos2𝜃 + C = cos−1𝑥4 2 𝑥2−1− 𝑥4 1− 𝑥2+C = 𝟐𝒙𝟐 − 𝟏𝟒 𝒄𝒐𝒔−𝟏𝒙− 𝒙𝟒 𝟏− 𝒙𝟐+𝐂
Ex 7.6
Ex 7.6, 2
Ex 7.6, 3
Ex 7.6, 4
Ex 7.6, 5
Ex 7.6, 6
Ex 7.6, 7
Ex 7.6, 8
Ex 7.6, 9 You are here
Ex 7.6, 10
Ex 7.6, 11
Ex 7.6, 12
Ex 7.6, 13 Important
Ex 7.6, 14 Important
Ex 7.6, 15
Ex 7.6, 16
Ex 7.6, 17
Ex 7.6, 18 Important
Ex 7.6, 19 Important
Ex 7.6, 20
Ex 7.6, 21
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Ex 7.6, 23
Ex 7.6, 24 Important
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