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Using the Trapezium rule with four ordinates (three strips), estimate to 4 significant figures the integral from 1 to 4 of (x^3+12)/4sqrt(x). Calculate the exact value of this integral, comparing it with your estimate. How could the estimate be improved?

Taking the value at the ordinates f(1) = 13/4, f(2) = 20/4sqrt(2), f(3) = 39/4sqrt(3), f(4) = 9.5 Then the trapezium rule states the integral is approximately 1/2 * [f(1) + 2f(2) + 2f(3) + f(4)], which (usin...
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Answered by Robert M. • Maths tutor
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Solve the simultaneous equations: x2 +y2 =5 and y = 3x + 1

x=-1, y=-2 x=2/5, y=11/5 or 2 and 1/5
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Answered by Emily H. • Maths tutor
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How do I differentiate a trigonometric function for something that is not just a single variable (e.g. d/dx (sin(3x))?

In order to differentiate a trig function with a term in front of the variable you are differentiating, you must use the chain rule. For example d/dx (sin (3x)) becomes 3cos(3x) because you have to multiply ...
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Answered by Kieran T. • Maths tutor
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What is De Moivre's theorem?

De Moivres theorem states that e^j(theta) = cos (theta) +jsin (theta) and this can be used to convert powered trig functions to the form of regular sines and cosines (i.e. sin^3(x) into a sum of terms includ...
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Answered by Kieran T. • Maths tutor
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Given that y = sin(2x)(4x+1)^3, find dy/dx

The product rule states that (uv)' = u'v + uv' Therefore we know that to find dy/dx we must have (sin(2x))'(4x+1)^3 +sin(2x)((4x+1)^3)' We can differentiate sin(2x) to 2cos(2x) and using the chain rule we ca...
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Answered by Myles M. • Maths tutor
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