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How to perform integration by substitution. (e.g. Find the integral of (2x)/((4+(3(x^2)))^2)) (10 marks)

We begin by looking at the integral by itself. The first thing we must do is evaluate what type of integration we should perform. It's always important to make sure that it's not a standard integral such ...

Answered by Kenneth B. • Maths tutor

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A function is defined as f(x) = x / sqrt(2x-2). Use the quotient rule to show that f'(x) = (x-2)/(2x-2)^(3/2)

u = x v = (2x-2)^(0.5)u' = 1 v' = (2x-2)^(-0.5)f'(x) = (vu' - uv') / v^2Therefore, f'(x) = (((2x-2)^(0.5) * 1) - (x * (2x-2)^(-0.5))) / ((2x-2)^(0.5))^2f'(x) = (2x - 2 - x) / (2x-2)^(3/2) = (x-2) / (2x-2)...

Answered by Isaac F. • Maths tutor

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Jay, Shelia & Harry share £7200 in the ratio 1:2:5. How much does Harry receive?

Explain how the ratio shows everyone's share of the £7200: 1:2:5 (Jay's share:Sheila's Share:Harry's Share)Add up the terms of the ratio to find out many equal parts the £7200 is split into: 1+2+5=8 (part...

Answered by Philip B. • Maths tutor

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A ladder of length 6.5m is leaning against a vertical wall. The foot of the ladder is 1.5m from the wall. Calculate the distance the ladder reaches up the wall to 3 significant figures.

(using Pythagoras' theorem) 6.5²= x²+ 1.5²x²= 6.5²- 1.5²x²= 42.25 - 2.25 x² = 40 x = sqrt(40) x ...

Answered by Pollyanna B. • Maths tutor

5520 Views

How to do Indices?

There are different rules when it comes to indices. First of all we will look at the example of multiplying two expressions . For example, y² x y⁴ . Here we need to do the addition r...

Answered by Taha H. • Maths tutor

3436 Views