Integration cos4 2x dx explain in great detail
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Integration cos4 2x dx explain in great detail

Integral of cos^4(x) (trigonometric identities + substitution)
Integral of cos^4(x) (trigonometric identities + substitution)

CBSE Class 12-science Answered

Integration cos4 2x dx explain in great detail

Asked by haroonrashidgkp | 06 Oct, 2018, 11:16: PM

begin mathsize 18px style integral cos to the power of 4 straight x space dx equals integral cos cubed straight x. cosx space dx equals sinx space cos cubed straight x plus 3 integral sin squared straight x space cos squared straight x space dx space equals sinx space cos cubed straight x plus 3 integral open parentheses 1 minus cos squared straight x close parentheses space cos squared straight x space dx equals sinx space cos cubed straight x plus 3 integral open parentheses cos squared straight x minus cos to the power of 4 straight x close parentheses space dx integral cos to the power of 4 straight x space dx equals sinx space cos cubed straight x plus integral 3 cos squared straight x space dx minus integral 3 cos to the power of 4 straight x space dx 4 integral cos to the power of 4 straight x space dx equals sinx space cos cubed straight x plus integral 3 cos squared straight x space dx equals fraction numerator sinx space cos cubed straight x over denominator 4 end fraction plus 3 over 4 integral cos squared straight x space dx now comma integral cos squared straight x space dx equals integral sinx space cosx space dx equals cosx space sinx space plus space straight x space minus integral cos squared straight x space dx integral cos squared straight x space dx equals fraction numerator cosx space sinx over denominator 2 end fraction plus straight x over 2 Substituting space in space the space expression space above straight I space equals equals fraction numerator sinx space cos cubed straight x over denominator 4 end fraction plus 3 over 4 open parentheses fraction numerator cosx space sinx over denominator 2 end fraction plus straight x over 2 close parentheses end style

Answered by Arun | 08 Oct, 2018, 11:47: AM

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Two dealers P and Q sell three items viz . , notebooks , pencils and erasers . In the month of April , the dealer P sells 250 notebooks , 400 pencils and 300 erasers , whereas the dealer Q sells 350 notebooks , 500 pencils and 470 erasers . In the month of may the dealer P sells 380 notebooks , 440 pencils and 360 erasers , whereas the dealer Q sells 450 notebooks , 520 pencils and 420 erasers.Using matrices represent The combined sale of two months for each dealer in each item ? ( i ) ( ii ) The change in sales from April to may for each dealer in each item ?question image

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