Calculate R8 for f(x)=10−x over [3,5]
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Given that,
f(x)=10−x
We have to calculate R8 over the interval [3 , 5]
Solution:
R8 = ∫ [3 , 5] f (x) dx
R8 = ∫ [3 , 5] (10 - x ) dx
R8 = ∫ [3 , 5] (10 x - x² / 2)
R8 = ∫ [3 , 5] (10 x ) - ∫ [3 , 5] ( x² / 2 )
R8 = [ 10 (5 - 3) ] - [ (5)² / 2 - (3)² / 2 ]
R8 = 10 (2) - [ 25 / 2 - 9 / 2 ]
R8 = 20 - (25 - 9) / 2
R8 = 20 - 16 / 2
R8 = 20 - 8
R8 = 12
Which is the required answer.
Hope this will helpful to you. Thanks.
Given that,
f(x)=10−x
We have to calculate R8 over the interval [3 , 5]
Solution:
R8 = ∫ [3 , 5] f (x) dx
R8 = ∫ [3 , 5] (10 - x ) dx
R8 = ∫ [3 , 5] (10 x - x² / 2)
R8 = ∫ [3 , 5] (10 x ) - ∫ [3 , 5] ( x² / 2 )
R8 = [ 10 (5 - 3) ] - [ (5)² / 2 - (3)² / 2 ]
R8 = 10 (2) - [ 25 / 2 - 9 / 2 ]
R8 = 20 - (25 - 9) / 2
R8 = 20 - 16 / 2
R8 = 20 - 8
R8 = 12
Which is the required answer.
Hope this will helpful to you. Thanks.
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