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Maths
A Level

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       ...

Answered by Will W. Maths tutor
35224 Views

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

ax2+bx+c=0 : basic quadratic equation

a(x+ bx/a) + c=0  

a((x+b/2a)-

Answered by Jaiveer D. Maths tutor
5463 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)/...

Answered by Daniel G. Maths tutor
51473 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 ...

Answered by Ben B. Maths tutor
7516 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=(x2+2x) and therefore y=eu

Then du/dx=2x+2 and d...

Answered by Duncan F. Maths tutor
12830 Views

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