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 ) −− −−− 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


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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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