(a) A curve has equation y = tan-¹4x (0 < x < Find the equation of the normal to the curve when x = 2. Write your answer in the form ax + by- (c + dπ) = 0 where a, b, c and d are integers. (b) Evaluate 36 15 1 √x² + 12x + 85 dx. Give your answer as a single logarithm in exact form. All working must be shown. - (c) Points A and B lie on the curve y = 6√x and have x coordinates 7 and 27 respectively. The y coordinates are positive in both cases. - axis. The arc AB is rotated 360° about the x - Find the area of the surface generated. Give your answer in terms of .
(a) A curve has equation y = tan-¹4x (0 < x < Find the equation of the normal to the curve when x = 2. Write your answer in the form ax + by- (c + dπ) = 0 where a, b, c and d are integers. (b) Evaluate 36 15 1 √x² + 12x + 85 dx. Give your answer as a single logarithm in exact form. All working must be shown. - (c) Points A and B lie on the curve y = 6√x and have x coordinates 7 and 27 respectively. The y coordinates are positive in both cases. - axis. The arc AB is rotated 360° about the x - Find the area of the surface generated. Give your answer in terms of .
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Q15
Transcribed Image Text:(a) A curve has equation y = tan-¹4x (0 ≤ x < 1)
-1.
Find the equation of the normal to the curve when x =
Write your answer in the form ax +by - (c + dπ) = 0 where a, b, c and d
are integers.
(b) Evaluate
86
15
1
√x² + 12x + 85
dx.
Give your answer as a single logarithm in exact form.
All working must be shown.
(c) Points A and B lie on the curve y = 6√x and havex - coordinates 7 and 27
respectively. The y coordinates are positive in both cases.
The arc AB is rotated 360° about the x - axis.
Find the area of the surface generated. Give your answer in terms of 7.
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Step 1: Find the equation of normal to the given curve
VIEWStep 2: Find the equation of normal to the given curve(continued)
VIEWStep 3: To evaluate the given definite integral
VIEWStep 4: To evaluate the given definite integral(continued)
VIEWStep 5: To find the area of surface generated
VIEWStep 6: To find the area of surface generated(continued)
VIEWStep 7: To find the area of surface generated(continued)
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