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By using partial fractions, integrate the function: f(x) = (4-2x)/(2x+1)(x+1)(x+3)

(4-2x)/(2x+1)(x+1)(x+3) = A/(2x+1) + B/(x+1) + C/(x+3) 4-2x = A(x+1)(x+3) + B(2x+1)(x+3) + C(2x+1)(x+1) let x = -1: 4-2(-1) = B(2(-1)+1)((-1)+3) 6 = B(-1)(2) B = -3 let x = -3: 4-2(-3)= C(2(-3)+1)((-3)+1) 10...
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Answered by Oliver F. • Maths tutor
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The velocity of a moving body is given by an equation v = 30 - 6t, where v - velocity in m/s, t - time in s. A) What is the acceleration a in m/s^2? B) Find the expression for the displacement s in terms of t given the initial displacement s(0)=10 m.

A) Acceleration is the rate of change of velocity with respect to time; therefore, in order to calculate it we need to differentiate the given equation of velocity v with respect to time t: a = dv / dt = d( ...
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Answered by Krisjanis P. • Maths tutor
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Expand and simplify (2x-2)(4x+6)

For this question the FOIL method can be used. FOIL stands for first, outside, inside, and last, and is used to make sure each term is multiplied by each other term. Firstly, multiply the first terms of each...
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Answered by Seren A. • Maths tutor
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How can I apply the chain rule for differentiation?

The chain rule needs to be applied when you are differentiating a function f of x with respect to a variable t, x is a function of (i.e. given f(x) and x(t), you want to calculate df/dt. To do so you will ha...
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Answered by Luca R. • Maths tutor
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Integrate 5sinxcosx + 5cosx

*Use identity sinxcosx = 1/2sin2x =5/2sin2x + 5cosx *then use simple integration gives =(-5/2 x1/2)cosx + 5sinx + c = =5/4cosx +5sinx + c
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Answered by Joanne A. • Maths tutor
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