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What is the integral of (6x^2 + 2/x^2 + 5) with respect to x?

When we think of integration, we should be thinking of the same method every time; adding one to the power, and then dividing by that new power.The integral of the sum of each of these terms is equal to the ...
WM
Answered by Wesley M. • Maths tutor
8642 Views

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
43006 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
6775 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
53848 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
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