Top answers

How do you solve a Differential equation using integrating factors?

Check the equation is in the form dy/dx + P(x) y=Q(x) (show example) Find the int factor: I(x)=e integralP(x) dx Multiply all terms by the integrating factorMake sure you show this step clearly: d/dx(I(x)y) ...
RB
Answered by Rachael B. • Maths tutor
3730 Views

The region below the curve y = e^x + e^(-x) and the lines x = 0, x = ln4 is rotated 2π radians about the x-axis. Find the volume of the resulting solid.

We can use the formula for a Volume of Revolution: V =π ∫ (e^x + e^(-x))^2 dx, with limits x = 0, x = ln4.Expanding the brackets: (e^x + e^(-x))^2 = e^2x + 2 + e^(-2x).So: V = π ∫ (e^2x + 2 + e^(-2x)) dx = π...
RS
Answered by Rumen S. • Maths tutor
4545 Views

What is the difference between a scalar product and a vector product, and how do I know which one to use in questions?

The main thing to consider here is the output of the operation. Vector and scalar products are both operations in which you take two vectors but then get something else. In a scalar product, you get a number...
ME
Answered by Maite E. • Maths tutor
9112 Views

Express x^2+2x+4 in the form (x+a)^2 + b, hence find the stationary point of the curve.

Step 1) x 2 +2x+4 = (x+1) 2 +3Step 2) Minimum point occurs at (-1, 3) I can use the whiteboard to explain it better.
AN
Answered by Anton N. • Maths tutor
7065 Views

Find the integral of the function y = ln(x)

(I can use the whiteboard for to explain it better)1) Express y = ln(x) as y = ln(x) * 12) Use integration by parts with u = ln(x), v'=(1), u'=1/x, v = xintegral = xln(x) - integral(x*1/x) =xln(x) - integral...
AN
Answered by Anton N. • Maths tutor
3694 Views