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∫ log(x) dx

Using "Integration by parts" or "reverse chain rule" . Recall formula for intergration by parts: "∫f'(x) g(x) dx = f(x)g(x) - ∫f(x)g'(x)dx" Then set f'(x) = 1, g(x) = log(x). Ca...
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Answered by Michael T. • Maths tutor
49406 Views

Differentiate f(x) = 2xlnx.

Use the chain rule: f'(x) = v(du/dx) +u(dv/dx). Let u = 2x, du/dx = 2, v = lnx, dv/dx = 1/x Using this information: f'(x) = 2lnx + 2x/x This simplifies to f'(x) = 2lnx +2.
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Answered by Tom V. • Maths tutor
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A simple circuit contains a battery rated at 12V, connected in series to a filament lamp with a resistance of 3 ohms. What current flows through the filament lamp?

V=IR, where V is voltage (volts), I is current (amps) and R is resistance (ohms). Since V and R are known, I needs to be found. Rearranging the equation gives: I=V/R. Inputting the values gives I=12/3. I=4A
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Answered by Tom V. • Physics tutor
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Find the solutions of the equation x^2 - 2x - 8 =0

First factorise the equation into 2 sets of brackets: You can do this by looking at the constant in the quadratic, 8. Try and find 2 numbers that multiply together to make 8 (such as 4 and 2), and that can b...
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Answered by Tom V. • Maths tutor
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I just arrived to the UK and I cannot keep up with my English classes. What can I do?

Listening & Speaking: get involved as much as you can with your class-mates. Learning a language by using it everyday is the quickest way to become fluent in it. Reading also helps a lot to understand sy...
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Answered by Giovanni B. • English tutor
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