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Find the volume of revolution when the curve defined by y=xe^(2x) is rotated 2*pi radians about the x-axis between x=0 and x=1

This is a standard question that may be found in a C4 mathematics paper. Students should use knowledge of the volume of revolution formula V = pi int_{a}^{b} y 2 dx to find the expression V = pi int_{0}^{1} ...
HS
Answered by Hanish S. • Maths tutor
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find the coordinates of the turning points of the curve y = 2x^4-4x^3+3, and determine the nature of these points

To begin, we must first use the fact that turning points of a graph occur at points where the gradient is equal to zero, in other words, points where dy/dx =0. Differentiating the equation with and setting t...
JN
Answered by Jenny N. • Maths tutor
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The equation kx^2 + 4x + (5 – k) = 0, where k is a constant, has 2 different real solutions for x. Show that k satisfies k^2-5k+4>0.

This questions is a proof type question, which means that you need to get to a specific formula. Usually, these questions give you clues in order to prove it. In this case it tells you that the equation has ...
AG
Answered by Alin G. • Maths tutor
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The equation of a curve C is (x+3)(y-4)=x^2+y^2. Find dy/dx in terms of x and y

Expand to get xy+3y-4x-12=x^2+y^2Rearrange to xy+3y-4x-12-x^2-y^2 Then you have to differentiate implicitly: use product rule on xy to get:u = x v =ydu = 1 dv = dy/dx so xy differentiates to xdy/dx + y Then ...
RR
Answered by Ravi R. • Maths tutor
4832 Views

Integration by parts; ∫e^x sin(x) dx

The first step in solving this problem is to identify that it is an integral that needs to be solved by parts. When you see an integral, check if it is in the form u v, where u and v are both functions of x ...
DB
Answered by Daniel B. • Maths tutor
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