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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 expr...

NM
Answered by Nick M. Maths tutor
5891 Views

Write the number 0.000000001 in standard form.

1 x 10^-9

AH
Answered by Abigail H. Maths tutor
18036 Views

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...

DS
Answered by Dimitris S. Maths tutor
9294 Views

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
5955 Views

simplify and rationalise 1/ sqrt(12)

  1. 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 squ...

MF
9975 Views

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