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What is the area under the graph of (x^2)*sin(x) between 0 and pi

To solve this integral you need to use integration by parts twice. You separate the two term in the integral into x^2 and sin(x). You then multiple x^2 by the integral of sin(x) (-cos(x)) and apply the upper...
KP
Answered by Khalil P. • Maths tutor
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A curve has parametric equations x = 1- cos(t), y = sin(t)sin(2t). Find dy/dx.

Here we have x(t) and y(t) which are both functions of t, but we want dy/dx, which doesn't involve t, we therefore need to use the chain rule. The chain rule tells us that: dy/dx = (dy/dt) x (dt/dx).y = sin(...
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Answered by William M. • Maths tutor
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Expand and simplify (x − 4)(2x + 3y)^2

following BIDMAS we start with the second expression by squaring it, i.e. (x-4)(2x + 3y)(2x + 3y). It is important we do it in the right order, otherwise we could get a wrong answer. We use the FOIL (First O...
EA
Answered by Elsie A. • Maths tutor
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Express (4x)/((x^2) - 9) - (2)/(x + 3) as a single fraction in its simplest form (4 marks)

To do this we need to find a common denominator. We have an (x + 3) on the right hand side and a difference of two squares ((x^2)-9) on the left hand side. So factorising what looks more complicated is first...
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Answered by Luke N. • Maths tutor
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solve 2^(3x+1)=16

The first step is to make sure that everything has the same base, so you can equate the powers. For example if you have an equation 2 2 = 2 x you know that x must equal 2. So with this question you can rewri...
JP
Answered by Jessica P. • Maths tutor
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