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Using the result: ∫(2xsin(x)cos(x))dx = -1⁄2[xcos(2x)-1⁄2sin(2x)] calculate ∫sin²(x) dx using integration by parts

Recall that ∫uv'=uv- ∫u'v Set u=sin²(x), v'=1 Therefore u'=2sin(x)cos(x) and v=x which gives us the following: ∫sin²(x)dx = xsin²(x) - ∫2xsin(x)cos(x)dx The second integral in the above expression is given i...
NM
Answered by Nick M. • Maths tutor
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Write the number 0.000000001 in standard form.

1 x 10^-9
AH
Answered by Abigail H. • Maths tutor
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solve 2cos^2(x) - cos(x) = 0 on the interval 0<=x < 180

we start y factoring and solving for each equation: cos(x) (2cos(x) - 1) = 0 this means: cos(x) = 0 and cos(x) = 1/2 from the first equation we get: x = 90 and from the second equation using the known trigon...
DS
Answered by Dimitris S. • Maths tutor
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Expand the brackets and simplify: 7(2x+3y)-x(14-y)

= 14x+21y-14x+xy =y(21+x)
IA
Answered by Ilan A. • Maths tutor
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simplify and rationalise 1/ sqrt(12)

Start by simplifying the denominator - We can write sqrt(12) as sqrt (4*3). - This can be written as sqrt(4) * sqrt(3) - We know the square root of 4 is 2. sqrt(3) is not a integer so we leave that as sqrt(3...
MF
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