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Study aid in Advanged level Mathematics... 27.J dx = "() +k B. 2 tan -G) +k C. 2 tan () +k D. 2 tan -(x) +k A. 2 tan Ma sin xcosxdx A. B.- C D. /2 %3! 29. x* Inxdx = A. 9ln3 B. 3ln3-3 C. 3ln3 -9 D. 9ln3-3

Study aid in Advanged level Mathematics... 27.J dx = "() +k B. 2 tan -G) +k C. 2 tan () +k D. 2 tan -(x) +k A. 2 tan Ma sin xcosxdx A. B.- C D. /2 %3! 29. x* Inxdx = A. 9ln3 B. 3ln3-3 C. 3ln3 -9 D. 9ln3-3

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Solve Q27, 28, 29 explaining detaiily each step

Study aid in Advanged level Mathematics.. 27. dx = 3+v? A. 2 tan )+k B. 2 tan -(+k C. 2 tan - (+k D. 2 tan (x) +k 28.2 sin xcosxdx = A. B. - c D 29. x* Inxdx= A. 9ln3 B. 3ln3-3 C. 3ln3 -9 D. 9ln3 - 3 30.f e dx = A. e* +k B. ex+1 + k 3x+1 C. e3x +k D. 3e3x + k 31.ſe*sinxdx = A. -½ e (cosx + sinx) + k C. e (cosx + sinx) + k 32. In(x²) dx = B. -e (cosx + sinx) + k D. - % e*cosx + k A. In4-2 B. 2ln4-2 C. In8 D. In16 +2 33.[ dx = 1+x2 A. In/l+ x/ +k C. tan'x-% In/1+x2/ + k 34.If x = tanu, (1+x*)² B. In /1+x - tan'x+k D. % In/1+x/ + tanx +k A.f 35.The area, in square units, of the region bounded by the curve: y (x + 2)(3–x) and the x- axis is: c 4 cosuduB. cos udu C.4 cos udu D. 2cosudu B 125 A. D. 36.The area, in square units, of the region defined by x- 2cose, y= 3sine, 0 ses 2r is: A. 6r B. 6 37.The are of the curve y x(x - 1)*for which 0 SXS2, y20 is rotated completely about the x-axis. The volume, in cubic units, enclosed by the surface generated is: A. 37 B. C. D. 4m C. 3m D. -6n 3 38.P and Q are the points on the curve x= at, y= given by 1= und t= 2. when the area beneath the arc PQ is rotated completely about the x-axis the volume, in cubie units, swept out is 2ma A. В. Зта C. 3na D. . 39.The region enclosed by the curve y =x+= and the lines y=½ x, x= 1 andx=2 is rotated about the x-axis. The volume, in cubic units, of solid of revolution is: 17 A. 4 D. C. 4m D. 40. The region bounded by the curve xy = 4, the x-axis and the ordinates x = 1 and x = 4 is rotated completely about the x-axis. The volume of the solid generated is C. 4n In 4 41.The area, in square units of the region defined by the inequalities iSy=2,0sxsy is: A. 47 B. 12n D. 4m In 3 A. B. V2 D. 50
Transcribed Image Text:Study aid in Advanged level Mathematics.. 27. dx = 3+v? A. 2 tan )+k B. 2 tan -(+k C. 2 tan - (+k D. 2 tan (x) +k 28.2 sin xcosxdx = A. B. - c D 29. x* Inxdx= A. 9ln3 B. 3ln3-3 C. 3ln3 -9 D. 9ln3 - 3 30.f e dx = A. e* +k B. ex+1 + k 3x+1 C. e3x +k D. 3e3x + k 31.ſe*sinxdx = A. -½ e (cosx + sinx) + k C. e (cosx + sinx) + k 32. In(x²) dx = B. -e (cosx + sinx) + k D. - % e*cosx + k A. In4-2 B. 2ln4-2 C. In8 D. In16 +2 33.[ dx = 1+x2 A. In/l+ x/ +k C. tan'x-% In/1+x2/ + k 34.If x = tanu, (1+x*)² B. In /1+x - tan'x+k D. % In/1+x/ + tanx +k A.f 35.The area, in square units, of the region bounded by the curve: y (x + 2)(3–x) and the x- axis is: c 4 cosuduB. cos udu C.4 cos udu D. 2cosudu B 125 A. D. 36.The area, in square units, of the region defined by x- 2cose, y= 3sine, 0 ses 2r is: A. 6r B. 6 37.The are of the curve y x(x - 1)*for which 0 SXS2, y20 is rotated completely about the x-axis. The volume, in cubic units, enclosed by the surface generated is: A. 37 B. C. D. 4m C. 3m D. -6n 3 38.P and Q are the points on the curve x= at, y= given by 1= und t= 2. when the area beneath the arc PQ is rotated completely about the x-axis the volume, in cubie units, swept out is 2ma A. В. Зта C. 3na D. . 39.The region enclosed by the curve y =x+= and the lines y=½ x, x= 1 andx=2 is rotated about the x-axis. The volume, in cubic units, of solid of revolution is: 17 A. 4 D. C. 4m D. 40. The region bounded by the curve xy = 4, the x-axis and the ordinates x = 1 and x = 4 is rotated completely about the x-axis. The volume of the solid generated is C. 4n In 4 41.The area, in square units of the region defined by the inequalities iSy=2,0sxsy is: A. 47 B. 12n D. 4m In 3 A. B. V2 D. 50
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