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Integrate sin^4(x)

sin^2(x) = (1 - cos(2x))/2 and cos^2(x) = (1 + cos(2x))/2so sin^4(x) = 0.25(1 - 2cos(2x) + cos^2(2x)) = 0.25(1 - 2cos(2x) + 0.5 + 0.5cos(4x))integrate = 3x/8 - sin(2x)/4 + sin(4x)/32
AN
Answered by Artem N. • Maths tutor
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How do I choose which term do I differentiate/integrate when I am integrating by parts

What you would do in this scenario is consider all the terms in the expression you are integrating. You then want to go through the acronym LATE to choose which term you should differentiate.L stands for Log...
FP
Answered by Federico P. • Maths tutor
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Integrate cos^2A

Integrating sin^2A and cos^2A is a bit nasty so we can use double angle formula to make it a little simpler. cos2A = cos^2A - sin^2A = 2cos^2A - 1. We can rearrange to get cos^2A in nicer terms. cos^2A = 1/2...
RM
Answered by River M. • Maths tutor
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A curve has parametric equations x= 2sin(t) , y= cos(2t) + 2sin(t) for -1/2 π≤t≤ 1/2π , show that dy/dx = - 2sin(t)+ 1

A parametric equation is where both x and y are expressed separately, in terms of a parameter (t). In order to differentiate them we must use the chain rule, which here would be dy/dx= dy/dt ÷ dx/dt. The dif...
KL
Answered by Katie L. • Maths tutor
15671 Views

find the diffrential of 3sin2x+4cos2x

dy/dx=6cos2x-8sin2xExplanation: cos x difrentiates to -sinx, we must times the coefficient of cos2x,(4) , by the differential of 2x (ie 2), giving -(4x2)sin2x.Similarly, sinx differentiates cosx, so using th...
AC
Answered by Amy C. • Maths tutor
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