if-f-x-x-16-x-2-3-find-0-5-3-5-f-x-dx-using-trapezoidal-method-then-find-the-max-and-min-value-of-the-error-with-the-given-n-steps-x-n-f-x-n-

Question Number 193036 by ali009 last updated on 02/Jun/23

i f f (x) = x \sqrt{{(16 - x^{2})}^{3}}

f i n d \int_{0.5}^{3.5} f (x) d x u s i n g t r a p e z o i d a l m e t h o d

t h e n f i n d t h e m a x a n d m i n v a l u e o f t h e e r r o r

w i t h t h e g i v e n n s t e p s

x_{n} f (x_{n})

- - - - -

0.5 31.24

0.93 54.69

1.36 72.3

1.79 81.98

2.21 81.25

2.64 71.54

3.07 51.68

3.5 25.41

Answered by MM42 last updated on 02/Jun/23

u_{f} = Σ u_{i} f \times Δ_{i} x = (54.69 + 72.3 + 81.98 + 81.25 + 71.54 + 51.68) \times 0.43 + 81.98 \times 0.42

= 212.2108

l_{f} = Σ l_{i} f \times Δ_{i} x = (31.24 + 54.69 + 72.3 + 81.25 + 71.54 + 51.68 + 25.41) \times 0.43 + 81.25 \times 0.42

= 211.9042

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