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2. The x-coordinate of the centriod of the area of the region defined by 0zy2x(x-1) 18 A. 1 B. C.2 D 10 3. The region bounded by the curve y x+ 4 the lines y 8 and x 0 is rotated through 2n radians about the x-axis. The y coordinate of the centriod of the solid formed is: A. 0 В. 10 C.- 20 D.-

2. The x-coordinate of the centriod of the area of the region defined by 0zy2x(x-1) 18 A. 1 B. C.2 D 10 3. The region bounded by the curve y x+ 4 the lines y 8 and x 0 is rotated through 2n radians about the x-axis. The y coordinate of the centriod of the solid formed is: A. 0 В. 10 C.- 20 D.-

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 Q42, 43 explaining detailly each step

dy aid in Advanced level Mathematics... 42. The x-coordinate of the centriod of the area of the region defined by 02 y2 N(X-1) I8 A. 1 B.유 C.2 D. 13. The region bounded by the curve y= x+ 4 the lines y 8 and x 0 is rotated through 2n radians about the x-axis. The y coordinate of the centriod of the solid formed is: A. 0 B. C. D. 20 . DIFFERENTIAL EQUATIONS 1. The equation of a curve which passes through the point (2, 1) and has gradient 2x-5 is: A. y=-5x+5 B. y=x-5x-4 C. y=+ y-1 D. y x -5x + 5 2. If 1 = dx 3-S then y= A. x- In(3-5x) +k B. In(3-5x) + k C. 1- 5ln(3-5x) +k D. 25 + k (3-5x) 3. The general solution of the differential equation du +1=u wherek is a constant is: dt A. u =t+k B. u=t+1+k C.u I+kt D. u 1- kt 4. Given that dy dx y+1 and that y = 1 when x = 0, then r+1 A. y - 2x+3 B. y = 2x +1 5. Given that 2 + x*y=x* and that y = 0 when x= 0, expressed in terms of x. y= C. y = 2x D. 2y = x+ 1 A. B. 1+ e*C. 1-e D. 1-e*- 6. The general solution of the differential equation 1 dy = In x is A. y = (In x) + k B. y =;+ Inx)+k C.y=(-+ in x) +k D. y = 2 In x + k 7. The general solution of the differential equation: dy 2x +2xy, where k is a constant is: dx A. y= e*+k - 1 B. y e*+k-1 C. y e+k+ 1 D. y= e+k 8. Ifu= 2 when x= 2, the particular solution of the differential equation ()= 1 is: dx A. u = x- In(x - 1) C. u =1+ In(x - 1) B. u=x + In(x-1) D.u x+ In(x - 1)+2 9. If (x+ 1) = 1-y and y = -3 when x 0 then y = A. B. -3 C. 4x +3 D. 4-4x x+1 10. Given that 2y- sin 2x = 0 and y = 0 when x 0, then y? = A.+ cos 2x 11. The general solution of the differential equation cosy = positive constant is: A. Y=sin'x 12. Given that y 1 when x = 2 the solution of the differential equation:(x - x) -v is 1-cos 2x C-2 cos 2x cos 2x D. dy 1 siny where k is a dx B. y= sin (kx)+:Cy= sin (1- kx) D. y sin (kx+1) dx 51
Transcribed Image Text:dy aid in Advanced level Mathematics... 42. The x-coordinate of the centriod of the area of the region defined by 02 y2 N(X-1) I8 A. 1 B.유 C.2 D. 13. The region bounded by the curve y= x+ 4 the lines y 8 and x 0 is rotated through 2n radians about the x-axis. The y coordinate of the centriod of the solid formed is: A. 0 B. C. D. 20 . DIFFERENTIAL EQUATIONS 1. The equation of a curve which passes through the point (2, 1) and has gradient 2x-5 is: A. y=-5x+5 B. y=x-5x-4 C. y=+ y-1 D. y x -5x + 5 2. If 1 = dx 3-S then y= A. x- In(3-5x) +k B. In(3-5x) + k C. 1- 5ln(3-5x) +k D. 25 + k (3-5x) 3. The general solution of the differential equation du +1=u wherek is a constant is: dt A. u =t+k B. u=t+1+k C.u I+kt D. u 1- kt 4. Given that dy dx y+1 and that y = 1 when x = 0, then r+1 A. y - 2x+3 B. y = 2x +1 5. Given that 2 + x*y=x* and that y = 0 when x= 0, expressed in terms of x. y= C. y = 2x D. 2y = x+ 1 A. B. 1+ e*C. 1-e D. 1-e*- 6. The general solution of the differential equation 1 dy = In x is A. y = (In x) + k B. y =;+ Inx)+k C.y=(-+ in x) +k D. y = 2 In x + k 7. The general solution of the differential equation: dy 2x +2xy, where k is a constant is: dx A. y= e*+k - 1 B. y e*+k-1 C. y e+k+ 1 D. y= e+k 8. Ifu= 2 when x= 2, the particular solution of the differential equation ()= 1 is: dx A. u = x- In(x - 1) C. u =1+ In(x - 1) B. u=x + In(x-1) D.u x+ In(x - 1)+2 9. If (x+ 1) = 1-y and y = -3 when x 0 then y = A. B. -3 C. 4x +3 D. 4-4x x+1 10. Given that 2y- sin 2x = 0 and y = 0 when x 0, then y? = A.+ cos 2x 11. The general solution of the differential equation cosy = positive constant is: A. Y=sin'x 12. Given that y 1 when x = 2 the solution of the differential equation:(x - x) -v is 1-cos 2x C-2 cos 2x cos 2x D. dy 1 siny where k is a dx B. y= sin (kx)+:Cy= sin (1- kx) D. y sin (kx+1) dx 51
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