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Maths
A Level

(FP3 question). Integrate 1/sqrt(3-4x-x^2).

There are two stages to this integral. Stage 1: Notice that there is a quadratic inside a square root in the denominator. We wish to look for a substitution which will reduce this problem...

Answered by Tristan G. Maths tutor
5808 Views

Find the stationary points of the curve f(x) =x^3 - 6x^2 + 9x + 1

Step One: stationary/turning points are points on the curve where the gradient equals 0 (i.e. a point at which the slope changes from negative to positive, or vice versa). So we ne...

Answered by Angharad L. Maths tutor
9411 Views

Solve the following equations. Leave answers in simplest terms a)e^(3x-9)=8. b) ln(2y+5)=2+ln(4-y)

a) Using log rules, a^x=b becomes log(a)b=x. If we take ln of both sides, we get ln(e^(3x-9))=ln8. ln(e) =1, so we just get 3x-9=ln8. Now we can simply manipulate this to get x=(9+ln8)/3=3+(1/3)ln8. Anoth...

Answered by Ben W. Maths tutor
6121 Views

a) show that (cosx)^2=8(sinx)^2-6sinx can be written as (3sinx-1)^2=2 b)Solve (cosx)^2=8(sinx)^2-6sinx

Start with a). Looking at this equation, the trig identity screaming out is cosx^2+sinx^2=1--> cosx^2=1-sinx^2. Substituting this into the LHS of the equation, and with a bit of algebraic rearrangement...

Answered by Ben W. Maths tutor
22369 Views

Integrate xsin(2x) by dx between the limits 0 and pi/2.

First it is important to identify that this is an integration by parts question as it can't be solved by substitution.
Let I = integral for ease of notation.Write out integration by parts formula I(...

Answered by Benedict A. Maths tutor
6480 Views

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