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How do you integrate the natural logarithm ln(x)?

To integrate this function, we must first recognise that ln(x) can be treated as 1 multiplied by ln(x). Using this knowledge, we can apply the 'integration by parts method' to integrate the function.Formula:...
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Answered by Andrew A. • Maths tutor
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Finding complex numbers using DeMoivre's Theorem

Find the cube roots of 2 1/2 cis(pi/4) 2 1/2 cis(pi/4+ 2pi k), for every integer k By DeMoivre: 2 1/2 1/3 cis((pi/4+ 2pi k)/3) 3 2 1/6 cis(pi/12+ 2/3 pi *k) Taking k=0,1,2 gives the three cube roots:z 1 = 2 ...
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Answered by Lisa R. • Maths tutor
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Differentiate y=(x-1)^4 with respect to x.

Using the chain rule, differentiate the "outside function" and the "inside function", and multiply the two results to get:dy/dx = 4(x-1)^3 * 1 = 4(x-1)^3
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Answered by Samuel H. • Maths tutor
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Find dy/dx in terms of t for the curve given by the parametric equations x = tan(t) , y = sec(t) for -pi/2<t<pi/2.

We know that dy/dx = (dy/dt) * (dt/dx). Differentiating each of the equations with respect to t gives. dy/dt = sec(t) tan(t) and dx/dt = sec 2 (t). Since dt/dx = 1 / (dx/dt) we have that dt/dx = 1/(sec 2 (t)...
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Answered by Oliver C. • Maths tutor
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7x+5y-3z =16, 3x-5y+2z=-8, 5x+3y-7z=0. Solve for x,y and z.

There are three methods to solve these types of silmultaneous equation questions, substitutution, elimination and matrices. In this example we use substitution and elimination.Elimination example.Eq1). 7x+5y...
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Answered by Holly May B. • Maths tutor
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