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Integrate (12x^5 - 8x^3 + 3)dx giving the terms of the answer in the simplest terms

Integration is essentially differentiation in reverse! So in the simpler cases instead of multiplying by the power of x and subtracting one from the power of x, you add one to the power of x and divide by th...
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Answered by Ellen S. • Maths tutor
7078 Views

(C3) Show that 4csc^2(x) - cot^2(x) = k can be expressed as sec^2(x) = (k-1)/(k-4) where k != 4

The student can answer this in several ways. One using the simple, known identities csc= 1/sin, cot=1/tan, sec=1/cos, tan=sin/cos, sin^2 + cos^2 = 1 and basic algebra is the following: 4csc^2 - cot^2 = k4/si...
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Answered by Fearghus H. • Maths tutor
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Find the binomial expansion of (-8+4x)^(2/3) up to and including the term in x^2.

The formula booklet is useful for this type of question, but only once we've rearranged the expression into the correct form. The formula booklet expression is: (1 + z)^n = 1 + n z + 0.5 n*(n-1) z^2 + .... T...
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Answered by David M. • Maths tutor
4821 Views

Explain the key purposes of the UN [15]

The United Nations was established through the San Francisco Conference in 1945 with current membership now at 193 states. It is the successor to the failed League of Nations. Its principle aims, spelled out...
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Answered by Nicholas G. • Politics tutor
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“Nations states are no longer the most significant actors in global politic” Discuss [45]

According to realism nation states provide the foundations for international relations, a principle primary based of Westphalianism, with esteemed political theorists such as Henry Kissinger agreeing with th...
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Answered by Nicholas G. • Politics tutor
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