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How do you integrate ln(x) with respect to x?

Rewrite ln(x) as 1 ln(x) then integrate by parts. The formula for integration by parts is ∫ uv' = uv - ∫ vu', here use u = ln(x) and v' = 1. By differentiating u we get u' = 1/x, and by integrating v' we get...
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Answered by Anthony G. • Maths tutor
3885 Views

Differentiate the function f(x) = sin(x)/(x^2 +1) , giving your answer in the form of a single fraction. Is x=0 a stationary point of this curve?

The key concepts to apply in this question will be the product and chain rules, namely: if f(x)=g(x)h(h), then f'(x)=g(x)h'(x) + g'(x)h(x), and if h(x)=u(v(x)), then h'(x)=u'(v(x))v'(x). Equivalently, you ma...
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Answered by Bromlyn C. • Maths tutor
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Show that: [sin(2a)] / [1+cos(2a)] = tan(a)

We start by expanding out the double trigonometric terms (sin(2a)) using the double angle formula, giving us: [2sin(a)cos(a)] / [1+cos^2(a) - sin^2(a)]. Next we spot that on the denominator (bottom half of f...
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Answered by George H. • Maths tutor
10160 Views

What does it mean when I get a negative value when I do a definite integral?

The definite integral gives the value of the area bounded between the curve at the given limits, and the x-axis (if we are integrating with respect to x!) If this value is negative, it means that the area un...
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Answered by Callum L. • Maths tutor
17792 Views

Differentiate y=x^2cos(x)

using the product rule product rule is dy/dx=v.du/dx+u.dv/dx let u = x^2 and v = cos(x) du/dx=2x dv/dx = -sin(x) so dy/dx=2xcos(x)-x^2sin(x)
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Answered by Ellen M. • Maths tutor
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