anonymous
  • anonymous
Integral with trig functions
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
|dw:1361089150658:dw|
dumbcow
  • dumbcow
i am intrigued
anonymous
  • anonymous
|dw:1361089181888:dw|

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anonymous
  • anonymous
or would it be cos^xcos5x
dumbcow
  • dumbcow
no cant combine them...it would just be \[\cos(5x) - \cos^{2} x \cos(5x)\]
anonymous
  • anonymous
ok
anonymous
  • anonymous
so left integral is easy
anonymous
  • anonymous
hmm no i cant do that
anonymous
  • anonymous
that 5x is just blowing my mind
dumbcow
  • dumbcow
yeah im not sure of way to do it without expanding out the cos(5x) ..... which would be messy
hartnn
  • hartnn
huh ? integral of cos 5x is just sin 5x/5 +c .
anonymous
  • anonymous
|dw:1361089595564:dw|
anonymous
  • anonymous
yA i know that integral, but its the cos^2 that is messin me up
hartnn
  • hartnn
ok, you need to used \(\sin^2x = (1- \cos2x )/2\)
anonymous
  • anonymous
okkk
hartnn
  • hartnn
then, for cos 2x cos 7x there is a standard formula for , cos A cos B =...
hartnn
  • hartnn
*cos 2x cos 5x
dumbcow
  • dumbcow
ahh i always forget sum to product rules ... anyway, here is solution http://www.wolframalpha.com/input/?i=integrate+sin^2%28x%29+cos%285x%29+dx
anonymous
  • anonymous
i got it then :)
hartnn
  • hartnn
good!
anonymous
  • anonymous
|dw:1361090139384:dw|
anonymous
  • anonymous
ok so here is another, im thinking with this one i can multiply by a 1/2 and use the identity sin2x
hartnn
  • hartnn
sin x cos x = (sin 2x) /2 then we have formula for sin A cos B
hartnn
  • hartnn
yes! good thought :)
anonymous
  • anonymous
nice!!
anonymous
  • anonymous
|dw:1361090244648:dw|
anonymous
  • anonymous
for the first question by parts can also be used . \[\Large \frac{1}{5}\sin^2(x)\sin(5x)-\frac{2}{5}\int\limits \sin(x)\sin(5x)\cos(x)dx\]
hartnn
  • hartnn
sin A cos B =... ?
anonymous
  • anonymous
oops
.Sam.
  • .Sam.
\[( \sin A ) ( \sin B )=\frac{1}{2} (\cos (A -B )-\cos (A +B ))\]
.Sam.
  • .Sam.
But there's still a lot of work if you do this
anonymous
  • anonymous
|dw:1361090429038:dw|
anonymous
  • anonymous
|dw:1361090501054:dw|
hartnn
  • hartnn
why - *minus* in between ?
anonymous
  • anonymous
integral of sin is -cosx
hartnn
  • hartnn
both of - from that you have factored out, right ? to make -1/4 ?
anonymous
  • anonymous
well, before i took integral
anonymous
  • anonymous
|dw:1361090806081:dw|
anonymous
  • anonymous
those will both be negative right?
hartnn
  • hartnn
integral of those will be negative, yes, right.
anonymous
  • anonymous
ok thats all i got, thank you so much both of you for helping me out, big test this friday
hartnn
  • hartnn
best of luck (Y)

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