Thread: solid of revolution and a matrix q

1. solid of revolution and a matrix q

Hi guys, not sure if anyone can help me but i'm super stuck with two uestions for my up coming exam:

Find the volume of the solid of revolution obtained by rotating, a full turn about the
x-axis, the area between the x-axis and the curve y = 2 sin x, for x
∈ [π/4, 3π/4].

and this one too

Matrices A, B, C , D & X satisfy equation A(X + B)C = D, and D is a 5×5 matrix. If A has 3 columns, and C 4 rows, ﬁnd the dimensions of each matrix. Give conditions on the matrices A, B, C & D, if necessary, to ensure that we can solve the above equation. Find an expression for the unknown matrix X .

Thanks very much

2. Originally Posted by kate45
Hi guys, not sure if anyone can help me but i'm super stuck with two uestions for my up coming exam:

Find the volume of the solid of revolution obtained by rotating, a full turn about the
x-axis, the area between the x-axis and the curve y = 2 sin x, for x
∈ [π/4, 3π/4].

and this one too

Matrices A, B, C , D & X satisfy equation A(X + B)C = D, and D is a 5×5 matrix. If A has 3 columns, and C 4 rows, ﬁnd the dimensions of each matrix. Give conditions on the matrices A, B, C & D, if necessary, to ensure that we can solve the above equation. Find an expression for the unknown matrix X .

Thanks very much

For the first one use the disk method the function represents the radius of a circular disk with thickness dx. so we get

$V=\int_{\frac{\pi}{4}}^{\frac{3\pi}{4}}\pi(\sin(x) )^2dx$

For part B

we know that Matrix X and B must have the same dimention (why?)

To multiply two matrices what conditions must be satisfied.