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Integrate the natural logarithm of x (ln x) with respect to x

In order to integrate ln x you have to use integration by parts, even though it appears there is only one term to be integrated. We get around this by instead writing it as (ln x)(1), where we treat the 1...

Answered by Archie D. • Maths tutor

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a) Express 4(cosec^2(2x)) - (cosec^2(x)) in terms of sin(x) and cos (x) and hence b) show that 4(cosec^2(2x)) - (cosec^2(x)) = sec^2(x)

A) 4(cosec²(2x)) - (cosec²(x)) = 4/(sin²(2x)) - 1/(sin²(x)) = 4/[(2 sin(x) cos(x))²] - 1/(sin²(x)) B) 4/[(2 sin(x) cos(x))²] - ...

Answered by Mario R. • Maths tutor

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2 Capacitors (c1 = 500mf) and (c2=300mf), are connected in parallel to a 10v d.c supply. Calculate the total capacitance of the circuit, and hence the total energy stored in the capacitors.

Use the equation Ct = C1 + C2, 500mF + 300mF = 800mF or 800x10^-3F
2) Appropriate equation is W=1/2 V^2 C
W = (0.5)*(10^2)*800^-3 = 40J

Answered by Samuel M. • Physics tutor

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A curve has equation y = f(x) and passes through the point (4, 22). Given that f'(x) = 3x^2 - 3x^(1/2) - 7, use integration to find f(x), giving each term in its simplest form

As we are given the derivative of f(x), we first need to integrate this derivative to obtain the function, f(x). Using the standard integration formula, ∫ x^n dx = (1/n+1)(x^(n+1)) +c, integrate each term...

Answered by Alex C. • Maths tutor

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How do I use an imperative?

Imperatives are used to give orders, express encouragement or give advice. They are formed from the present tenses forms of verbs of the second person singular (tu), second person plural (vous) and the fi...

Answered by Amelia D. • French tutor

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