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sec? Show that sec x cosec x = sec x 2 a tan x TC b Hence, or otherwise, find the exact value of Cosec x secx dx. TO 4

sec? Show that sec x cosec x = sec x 2 a tan x TC b Hence, or otherwise, find the exact value of Cosec x secx dx. TO 4

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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Show that f(x) = x' + x is an odd function. %3D b Hence find the value of f(x) dx. Find the total area between y = f(x), the x-axis and the lines x =-2 Show that sec x cosec x = tan x b Hence, or otherwise, find the exact value of . Cosec x sec x dx. 3 Find the area enclosed between the curves y = (x- 1) and y = 5 - x. %3D 4 Find the exact value of |8 sec 2x dx. 12 1. 5 Evaluate (3x²-4) 6 Use the trapezoidal rule with 4 subintervals to find the area enclosed b the y-axis and the lines y = 1 and y = 3. %3D %3D x-2' Sketch the curve y= x(x- 1)(x + 2). %D Find the total area enclosed between the curve and the x-axis. 8 Find the area bounded by the parabola y = x and the line y = 4-x corn 2 decimal places. %3D Find the derivative of xVx+ 3. X +2 Hence find | - dx. b. Vx+3 Find (x²In x). xp
Transcribed Image Text:Show that f(x) = x' + x is an odd function. %3D b Hence find the value of f(x) dx. Find the total area between y = f(x), the x-axis and the lines x =-2 Show that sec x cosec x = tan x b Hence, or otherwise, find the exact value of . Cosec x sec x dx. 3 Find the area enclosed between the curves y = (x- 1) and y = 5 - x. %3D 4 Find the exact value of |8 sec 2x dx. 12 1. 5 Evaluate (3x²-4) 6 Use the trapezoidal rule with 4 subintervals to find the area enclosed b the y-axis and the lines y = 1 and y = 3. %3D %3D x-2' Sketch the curve y= x(x- 1)(x + 2). %D Find the total area enclosed between the curve and the x-axis. 8 Find the area bounded by the parabola y = x and the line y = 4-x corn 2 decimal places. %3D Find the derivative of xVx+ 3. X +2 Hence find | - dx. b. Vx+3 Find (x²In x). xp
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