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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 we'...
LD
5236 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 highlig...
LN
6125 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 called neurotransmitters . - The neu...
SI
Answered by Saira I. • Biology tutor
3387 Views

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

u=x 2 + 3 du/dx=2x dx=du/2x 2x/(x 2 +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 2 +3)+c
TS
Answered by Tom S. • Maths tutor
14876 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% (less...
HC
Answered by Harry C. • Economics tutor
2160 Views