8. Find the areas of the surfaces generated by revolving the curves: (a) x=2/4-y, 0sys15/4 about the y-axis. (b) x= /2y-1, 0sys15/4 about the y- axis. See figures for part (a) and (b) respectively. 15/4 (1, 15/4) (1, 1) x 2V4-y x = V2y- 1 5) 1/2

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Author:James Stewart
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Chapter1: Functions And Models
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Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Answer question 8
1. Find the differential equation of the family of circles of radius r whose centre lies
on the x-axis.
2. Form the differential equation from the function: y= Ae * + Be
3. Solve the given differential equations:
x² + y
dy
=1. (ii)
dx
dy
dy
+2x=x1-x²
dx
y+.
(i) ху(1+ ху?)
(ii) (1-х*)
dx
4. Use integration by parts to compute the following:
(i) Í(2x-x)e*dx (ii) Íxcos xsin xdx
(iii) (xtan xdx (iv) fx tan xdx
5. Evaluate the following integrals:
sin x
(1) +3x + 2
dx (ii) [ Vsin x cos xdx (i)
„dx (iv) Na"-
- x² dx
V1+ cos x
6. Find the area of the circle 4x +4y =9 which is interior to the parabola y = 4x.
7. Find the volume formed by the revolution of the loop of the curve y'(a+ x) =x'(3a - x)
about the x-axis.
8. Find the areas of the surfaces generated by revolving the curves:
(a) x=2/4-y, 0s y<15/4 about the y-axis. (b) x= 2y-1, 0<y<15/4 about the y-
axis. See figures for part (a) and (b) respectively.
15/4
(1, 15/4)
(1, 1),
x 2V4-y
x = V2y - 1
Transcribed Image Text:1. Find the differential equation of the family of circles of radius r whose centre lies on the x-axis. 2. Form the differential equation from the function: y= Ae * + Be 3. Solve the given differential equations: x² + y dy =1. (ii) dx dy dy +2x=x1-x² dx y+. (i) ху(1+ ху?) (ii) (1-х*) dx 4. Use integration by parts to compute the following: (i) Í(2x-x)e*dx (ii) Íxcos xsin xdx (iii) (xtan xdx (iv) fx tan xdx 5. Evaluate the following integrals: sin x (1) +3x + 2 dx (ii) [ Vsin x cos xdx (i) „dx (iv) Na"- - x² dx V1+ cos x 6. Find the area of the circle 4x +4y =9 which is interior to the parabola y = 4x. 7. Find the volume formed by the revolution of the loop of the curve y'(a+ x) =x'(3a - x) about the x-axis. 8. Find the areas of the surfaces generated by revolving the curves: (a) x=2/4-y, 0s y<15/4 about the y-axis. (b) x= 2y-1, 0<y<15/4 about the y- axis. See figures for part (a) and (b) respectively. 15/4 (1, 15/4) (1, 1), x 2V4-y x = V2y - 1
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