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Find, without using a calculator, integral of 1/sqrt(15+2x-x^2) dx, between 3 and 5, giving your answer as a multiple of pi

To get the denominator into something usable, you have to complete the square so you have it in one of the forms you can use a trig or hyperbolic substitution for. The minus sign in front of the x2 means ...

Answered by Luke D. • Further Mathematics tutor

4087 Views

How do I analyse unseen poetry?

When you first read a poem, it's important to put on your detective hat! It's almost like arriving at a crime scene for the first time.To be a great detective you need to be prepared! Bring a pen and high...

Answered by Lucy N. • English Literature tutor

4948 Views

Describe how a synapse works

- An electrical impulse travels down the axon of a pre-synaptic neurone. - The movement of this electrical impulse initiates the release of chemical messengers which are...

Answered by Saira I. • Biology tutor

2735 Views

Integrate 2x/(x^2+3) using the substitution u=x^2+3

u=x² + 3

du/dx=2x

dx=du/2x

2x/(x²+3) dx becomes (2x/u) * (du/2x)

the 2x terms cancel out giving 1/u du

this integrates to ln(u)+c becoming ln(x

Answered by Tom S. • Maths tutor

13230 Views

If timber prices fall by 30%, what will be the expected % change in demand for timber in the economy if the Price Elasticity of Demand is -0.5, and explain the effect on revenue for a timber-selling firm.

Price Elasticity of Demand (PED) is a measure of the responsiveness of demand to a change in price. A PED of -0.5 suggests demand is price inelastic – as Price falls by 1%, Demand will increase by 0.5% (l...

Answered by Harry C. • Economics tutor

1748 Views