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Need help to evaluate integral?

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Need help to evaluate integral? 

asked Dec 8, 2014 in CALCULUS by anonymous

1 Answer

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Given function  46 ( t + 9 ) ( t – 2 )6

Apply formula ∫UVdx = U∫Vdx - ∫(dU/dx)(∫Vdx)dx

=  (t + 9) ∫ (t – 2)6 - ∫ (d/dt) (t + 9) ∫ (t – 2)dt

= (1/7)(t + 9) (t – 2)7 - ∫ (1) (1/7) (t – 2)dt

= (1/7)(t + 9) (t – 2)7 - (1/7)∫ (t – 2)dt

= (1/7)(t + 9) (t – 2)7 - (1/7)(1/8) (t – 2)8

= (1/7)(t + 9) (t – 2)7 - (1/56) (t – 2)8

Apply limits  (  lower limit = 4 , upper limit = 6  )

= (1/7) [ (6 + 9) (6 – 2)7 - (4 + 9) (4 – 2)7 ] - (1/56) [ (6 – 2)8 - (4 – 2)8 ]

= (1/7) [ (15)(4)7 - (13)(2)7 ] - (1/56) [(4)8 - (2)8]

= (1/7) [ (15) (16384) - (13) (128) ] - (1/56) [ (65536) - (256) ]

= (1/7) [ 245760 - 1664 ] - (1/56) [ 65280 ]

= (1/7) [ 244096 ] - (1/7) [ 8160 ]

= (1/7) (244096 – 8160)

= (1/7) (235936)

= 235936/7

Solution : 46 ( t + 9 ) ( t – 2 )6 = 235936/7.

answered Dec 8, 2014 by Shalom Scholar
edited Dec 8, 2014 by yamin_math

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