Question

In estimating

cos(5)d using Trapezoidal and Simpson's rule with n = 10, we can estimate the error
involved in the approximation using the Error Bound formulas.
For Trapezoidal rule, the error will be less than
For Simpson's rule,the error will be less than
Give your answers accurate to at least 2 decimal places

Answer 1

The error bound for the Trapezoidal rule can be estimated using a formula, and the error bound for Simpson's rule can be estimated using another formula. Substitute the given values into these formulas to find the estimated errors.

Step-by-step explanation:

The error bound for the Trapezoidal rule can be estimated using the formula:

Error <= [-(b-a)^3/(12n^2)]*f''(c),

where a and b are the limits of integration, n is the number of subintervals, and f''(c) is the second derivative of the function evaluated at some point c in the interval [a, b].

For Simpson's rule, the error bound is given by the formula:

Error <= [-(b-a)^5/(180n^4)]*f''''(c),

where a, b, n, and f''''(c) have the same meanings as in the Trapezoidal rule formula.

In this case, substitute a = 0, b = 5, n = 10, and the appropriate second and fourth derivatives of the function cos(x) into the respective error bound formulas to find the estimated errors.