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∫ x^3 *ln(2x) (from 2->1) can be written in the form pln 2 + q, where p and q are rational numbers. Find p and q.

Firstly I would think about how I could integrate this. In this case you would need integrate by parts. I use LATE to decide which value is u and v' which stands for Log,Algebra,Trig,Exp. Which ever one appe...
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If the velocity of a particle is given by t^2+t, then determine the acceleration of the particle when t=4.

To get from velocity to acceleration, you must derivate the velocity equation. This is because acceleration is the rate at which velocity changes so to change the velocity into acceleration it must be derive...
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How do I check if events are independent (in statistics / probability)?

The sentence 'event A is independent to event B' means that the probability of A does not affect the probability of event B. In mathematical terms, this can be written as:Prob(A and B) = Prob(A) x Prob(B) So...
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Integrate Sin(2X)

-1/2 Cos(2X)
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Problem of Optimisation: A company is designing a logo. The logo is a circle of radius 4 inches with an inscribed rectangle. The rectangle must be as large as possible.

First, draw a diagram showing the rectangle, the circle and the unknowns . Then find the equations representing this problem (equation of a circle of center 0, x 2 +y 2 =4 2 (1) and of the area of the rectan...
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