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Compute the integral of f(x)=x^3/x^4+1

A basic function of integration states that: for a function f(x), the integral of f'(x)/f(x) = ln[f(x)] (the natural log of the modulus of f(x)). Take the denominator of f(x), x 4 +1. We will refer to this a...
TD
Answered by Tyla D. • Maths tutor
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When do you use the present continuous in Italian?

The presend continuous in Italian is used for an action that is taking place at the time of speaking. For example: "sto mangiando una mela": I am eating an apple, this means that you are eating the...
CP
Answered by Chiara P. • Italian tutor
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A curve has parametric equations x = 1 - cos(t), y = sin(t)sin(2t) for 0 <= t <= pi. Find the coordinates where the curve meets the x-axis.

If the curve is meeting the x-axis, notice that this means y = 0. So we must solve sin(t)sin(2t) = 0 for t within the given bounds. Using a trigonometric identity sin(2t) = 2cos(t)sin(t), we obtain sin 2 (t)...
CB
Answered by Callum B. • Maths tutor
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How does Angela Carter's "The Bloody Chamber" rewrite gothic tales according to a feminist agenda?

Carter's intentions for reimagining of the Gothic genre in her 1979 collection of short stories The Bloody Chamber can be more clearly understood when considering her political motives - she was a second-wav...
AL
Answered by Alex L. • English tutor
8828 Views

Why is the integral of 1/sqrt(1-x^2)dx = sin^{-1}(x)?

This is an example of an integral that uses trigonometric substitutions, which is quite a common theme for A-level further maths questions. Firstly, notice the denominator is quite unpleasant, so to make thi...
CB
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