The trapezoidal rule applied on <msubsup> &#x222B;<!-- ∫ --> 0 <mrow class="MJX-T

letumsnemesislh 2022-07-10 Answered
The trapezoidal rule applied on 0 2 [ f ( x ) ] d x gives the value 5 and the Midpoint rule gives the value 4. What value does Simpson's rule give?
You can still ask an expert for help

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Answers (1)

gozaderaradiox5
Answered 2022-07-11 Author has 19 answers
First of all, f ( 1 ) should be 2 since midpoint rule gives you 2 f ( 1 ) = 4. You also know that f ( 0 ) + f ( 2 ) = 5. So
S = 1 3 [ f ( 0 ) + 8 + f ( 2 ) ] = 8 3 + 1 3 5 = 13 3

We have step-by-step solutions for your answer!

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

You might be interested in

asked 2022-06-13
Prove: Let S ( n ) and T ( n ) be the approximations of a function using n intervals by using Simpson's rule and the Trapezoid rule respectfully.
S ( 2 n ) = 4 T ( 2 n ) T ( n ) 3
asked 2022-05-10
Show that one extrapolation of the trapezoid rule leads to Simpson's rule.
asked 2022-07-05
Use both trapezoid and Simpson's rule to find 0 e x d x starting with h = 2 where h is the length of subintervals [ x i , x i + 1 ].
asked 2022-06-21
Relation between Simpson's Rule, Trapezoid Rule and Midpoint Rule.
How 2 n numbers come out at the left side while only n numbers at the right side.
asked 2022-05-10
Let
F ( x ) = x f ( t ) d t ,
where x R , f 0 is complicated (it cannot be integrated analytically).
Can we used the Simpson's rule to approximate this integral, knowing that f ( ) = 0?
asked 2022-05-13
How to derive the quadrature weights for the trapezoid and the Simpsons rule?
Trapeziod rule: a b f ( x ) b a 2 [ f ( a ) + f ( b ) ]
Simpson's rule: a b f ( x ) b a 6 [ f ( a ) + 4 f ( ( a + b ) / 2 ) + f ( b ) ]
asked 2022-06-14
The error bound formulas for trapezoidal rule and simpson's rule say that:
Error Bound for the Trapezoid Rule: Suppose that  Error Bound for the Trapezoid Rule: Suppose that  | f ( x ) | k  for some  k R  where  a x b .  Then  | E T | k ( b a ) 3 12 n 2  Error Bound for Simpson's Rule: Suppose that  | f ( 4 ) ( x ) | k  for some  k R  where  a x b .  Then  | E S | k ( b a ) 5 180 n 4
Using these formulas, is it possible to find functions where Trapezoid Rule is more accurate than Simpson's rule?

New questions