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The finite region bounded by the x-axis, the curve with equation y = 2e^2x , the y-axis and the line x = 1 is rotated through one complete revolution about the x-axis to form a uniform solid. Show that the volume of the solid is 2π(e^2 – 1)

The volume of revolution, V, is given as 2π∫ydx Substituting in the equation and limits gives as follows: V = 2π∫2e^2x dx between 0 and 1 Integrating this gives V = 2π[e^2x] between 0 and 1 Applying the ...

Answered by Michael C. • Further Mathematics tutor

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How do I find the vector/cross product of two three-dimensional vectors?

Finding the cross product of two 3D vectors uses a very similar method to that of finding the determinant of a 3x3 matrix.

So, to find the cross product, just follow these simple steps:

Answered by Luke M. • Further Mathematics tutor

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Find the general solution for the determinant of a 3x3 martix. When does the inverse of this matrix not exist?

Let M be a 3x3 matrix s.t. M= |a b c| |g h i| |d e f|

Then Det(M)= a(Det(e,f,h,i))-b(Det(d,f,g,i))+c(Det(d,e,g,h).

Given that the determinant of a 2x2 matrix such as (e,f,h,i) is = ei-fh. Th...

Answered by Oskar D. • Further Mathematics tutor

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Find the general solution to the second order differential equation x'' - 2x' + x = e^(2t).

Firstly, note that the question only asks for the general solution (G.S.) to the equation, not for the whole solution. Now we have established what we need to find, construct the auxiliary equation. For t...

Answered by Amy B. • Further Mathematics tutor

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Find the modulus-argument form of the complex number z=(5√ 3 - 5i)

The easiest way to complete questions of these types is to first sketch an Argand diagram. With 5√ 3 on the x (real) axis and -5 on the y (imaginary) axis, the modulus would be calculated simply by using ...

Answered by Chris P. • Further Mathematics tutor

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