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Integrate 5sinxcosx + 5cosx

*Use identity sinxcosx = 1/2sin2x =5/2sin2x + 5cosx *then use simple integration gives =(-5/2 x1/2)cosx + 5sinx + c = =5/4cosx +5sinx + c
JA
Answered by Joanne A. • Maths tutor
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Express (5-√ 8)(1+√ (2)) in the form a+b√2 , where a and b are integers

5 + 5√ 2 - √ 8 - √ 16 (Break up all terms in terms of square roots of 2) 5 + 5√ 2 - √ 8 - 4 5 + 5√ 2 - 2 √ 2 - 4 1 + 3√2
IM
Answered by Ignacio M. • Maths tutor
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Differentiate "sin(2x)"

Sinx differentiates to give cosx. We then multiply this by the differential of "2x." Which equals 2. Our answer therefore is "2cos(2x)."
CB
Answered by Ciaran B. • Maths tutor
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Find the area between the curves y = x^2 and y = 4x - x^2.

First, we need to draw a diagram , to understand the question more clearly. y = x^2 is a common curve, but to sketch y = 4x - x^2, we should factorise it, to find where it inersects the x-axis. 4x - x^2 = x(...
LM
Answered by Lamisah M. • Maths tutor
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Two particles A and B of mass 2kg and 3kg respectively are moving head on. A is moving at 5m/s and B is moving at 4m/s. After the collision, A rebounds at 4m/s. What is the speed of B and what direction is it moving in?

Using conservation of momentum, m1u1 + m2u2 = m1v1 + m2v2, set m1 = 2kg, m2 = 3kg, u1 = 5m/s, u2 = -4m/s and v1 = -4m/s. Substitute these into the equation to get 2 5 + 3 (-4) = 2*(-4) + 3*v2 10 - 12 = -8 +3...
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Answered by Amber S. • Maths tutor
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