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Integrate y=(x^2)cos(x) with respect to x.

This problem must be solved using integration by parts, since y is equal to the product of two functions of x. Let u=x^2, therefore u'=2x (u'=du/dx). Let v'=cos(x), therefore v=sin(x) (v'=dv/dx).Using the in...
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Answered by Antony H. • Maths tutor
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Which of the fractions 6/12, 9/8, 2/3 is equivalent to 12/18?

You want to look for 12/18 in its minimal form, meaning that you cannot divide the numerator and denominator by the same number, unless that number is 1. So try to work out what the numbers are that divide b...
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Answered by Emily S. • Maths tutor
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Differentiate with respect to x: (x^2+5)^3

There are two methods for solving this question. Firstly, the inspection method, and then the chain rule method.Using the inspection method, we differentiate the outer function first. Multiply the function b...
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Answered by Matthew P. • Maths tutor
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What is the equation of the tangent to the circle x^2 + y^2 = 25 at the point (-3, -4)?

From circle theorems, the tangent to a circle is perpendicular to the radius, and so to find the tangent we can use the gradient of the radius connecting the point (-3, -4) to the centre of the circle and th...
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Answered by Rebecca A. • Maths tutor
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(6^2 + 8^2)^1/2 = (125a^3)^1/3 Work out the value of a?

(6 2 + 8 2 ) 1/2 = (125a 3 ) 1/3 (36+62) 1/2 = (125a 3 ) 1/3 100 1/2 = (125a 3 ) 1/3 +/- 10 = (125a 3 ) 1/3 Using +10 as the left-hand side answer:10 = (125a 3 ) 1/3 1000 = 125a 3 8 = a 3 2 = aUsing -10 as t...
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Answered by Kate S. • Maths tutor
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