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How do I integrate the volume of revolution between 0 and pi of y=sin(x)?

To integrate the volume of revolution first imagine a thin disk around the x-axis which we want to know the volume of: Volume=area x height. The area of a circle is given by pi r^2 and in our case let us use...
LC
Answered by Luke C. • Maths tutor
4388 Views

Solve: x^2-7x+6=0

Factorise the equation and then equate each set of brackets to 0 to obtain both possible solutions. By factorising: (x-6)(x-1)=0 Therefore: x=6 or x=1
PG
Answered by Phoebe G. • Maths tutor
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Line AB has equation 4x+5y+2=0. If the point P=(p, p+5) lies on AB, find P . The point A has coordinates (1, 2). The point C(5, k) is such that AC is perpendicular to AB. Find the value of k.

i) Well, if point P lies in AB, then the value of its x and y coordinates have to fulfill the condition imposed by equation AB. Therefore, substituting the x value p for x and the y value p+5 for y: 4(p)+5(p...
JL
Answered by Javier L. • Maths tutor
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(A-Level) Find the coordinate of the stationary point of the curve y = 2x + 27/x^2

Since we are looking for a stationary this means the derivative will be equal to 0, so we will have to differentiate the equation. When we differentiate ( y = 2x + 27/x^2 ) we get ( dy/dx = 2 - 54/x^3 ). Bec...
VB
Answered by Vlad B. • Maths tutor
7487 Views

Integrate a^x with respect to x

This comes up in C4 in A level maths and differentiating it could come up in C3. You can write a^x as exp(ln(a^x))=exp(xln(a)) then differentiating this, you get ln(a) exp(xln(a))=ln(a)a^x. By differentiatin...
JW
Answered by John W. • Maths tutor
40931 Views