In November 2024
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) Solve the area bounded by the curve y = 4x-x² and the lines x = -2 and y = 4.
Find the area, take the elements of the area parallel to the x-axis. y= 2x³-3x³-9x; y=x²-2x²-3x.
Water is flowing into a conical vessel 18 cm deep and 10 cm across the top at the rate of 4 cm3/min. The depth of the water is "h" cm. If the rate which the surface is rising is 0.1146 cm/min, find the value of "h"?
write (2-i)(4-3i)^2/3+2i in the form a+bi where a,b,er.
1) Find the area bounded by the curve y=9-x and the x axis.
a) Horizontal Strip
b) Vertical Strip
Calculate the definite integral y = 𝑡 ^3 + 2𝑒 ^ 4𝑡 + 1/ 𝑡 + 3 sin 2𝑡)
CENTROID OF SOLID REVOLUTION:
The region of the 1st quadrant which is bounded by the curve x2 = 4y, the line x = 4, is revolved about the line x = 4, Locate the centroid of the resulting solid of revolution
A particle start from rest and moves in a straight Line on a smooth horizontal surface.The speed of the particle given that V=e^2-1/4 when t=1.Show that V=1/4(e^2t-1)
1. Find the volume of the solid generated by revolving the region between the parabola
x = y² + 1 and the line x = 3 about the line x = 3.
2. Find the area of the region bounded above by the curve 𝑦 = 2𝑒^−𝑥 + 𝑥, below by the curve y =𝑒/𝑥 2, on the left by x = 0, and on the right by x = 1
Differentiate the trigonometric functions
1. = 2 sec x + tan x
2. y = sin x/ 1 + COS X
3. y = cos x cot x
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