Top answers

How do you integrate (sinx)^2?

(sinx)^2 (similarly to (cosx)^2) cannot be integrated in this form. There is a standard method to get past this though, which makes use of the cos double angle formula:cos(2x) = (cosx)^2 - (sinx)^2 = 1 - (si...
WW
Answered by Will W. • Maths tutor
43307 Views

Derive from the standard quadratic equation, the form of the quadratic solution

ax 2 +bx+c=0 : basic quadratic equation a(x 2 + bx/a) + c=0 a((x+b/2a) 2 - b 2 /4a 2 ) + c=0 (retain equation with only one x variable; compensate for b term squared out with term - b 2 /4a 2, ) a(x+b/2a) 2 ...
JD
Answered by Jaiveer D. • Maths tutor
6873 Views

Write tan(3x) in terms of tan(x). Hence show that the roots of t^3 - 3t^2 - 3t + 1 = 0 are tan(pi/12), tan(5pi/12) and tan(3pi/4)

The first part is relatively simple. If we write tan(3x) as tan(2x+x) we can use addition formulae to give: tan(2x+x)= (tan(2x)+tan(x))/(1-tan(2x)tan(x)) tan(2x) = 2tan(x)/(1-tan^2(x)) Substituing this in an...
DG
Answered by Daniel G. • Maths tutor
53971 Views

differentiate y = (4-x)^2

This is a basic example of a very important result: the chain rule. The difficulty of this sort of example is that we have a "function of a function". That is, we have the function '4-x' and then w...
BB
Answered by Ben B. • Maths tutor
8805 Views

Differentiate y=e^(x^2+2x)

For this question the chain rule should be used, the chain rule is that dy/du*du/dx=dy/dx. If we say u=(x 2 +2x) and therefore y=e u Then du/dx=2x+2 and dy/du=e u. Then dy/du*du/dx= (2x+2)e u , then we can s...
DF
Answered by Duncan F. • Maths tutor
15548 Views