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Integrate x^2sin(x) between -pi and pi

It is possible to solve this question using integration by parts. However, we note that sin(x) is an odd function, meaning that sin(-x) = -sin(x). Thus x2sin(x) is also an odd function. This me...

HL
6028 Views

Explain the Rule of Law doctrine.

1) Definition of the Doctrine

The Rule of Law (ROL) is one of the three central doctrines of the English constitution, alongside the Separation of Powers and Parliamentary Sovereignty. It wa...

AJ
Answered by Arron J. Law tutor
19590 Views

Complete the following nuclear equation p+ -----> n + ... + ...

This is a proton decaying into a neutron and two other subatomic particles. Here you have to consider various conservation laws, including: baryon number, lepton number and charge. (Energy and momentum ar...

RS
Answered by Ryan S. Physics tutor
3700 Views

The potential difference in a circuit is 5V. There are two resistors connected in series of resistance 10 Ohms. Calculate the current I in the circuit.

Ohm's law states that V=IR ; where V is p.d., I is current and R is resistance.

Firstly the two resistors are in series so the total resistance is just the sum of the two resistanc...

RS
Answered by Ryan S. Physics tutor
4453 Views

Consider the functions f and g where f (x) = 3x − 5 and g (x) = x − 2 . (a) Find the inverse function, f^−1 . (b) Given that g^−1(x) = x + 2 , find (g^−1 o f )(x) . (c) Given also that (f^−1 o g)(x) = (x + 3)/3 , solve (f^−1 o g)(x) = (g^−1 o f)(x)

(a) Start with f(x)= 3x − 5; y=3x - 5, and switch x and y before rearanging to get y in terms of x again:

y=3x - 5

x=3y - 5

(x+5)/3=y

Therefore f^−1(x)=(x+5)/3

(b) Start...

IB
Answered by Isobel B. Maths tutor
19021 Views

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