Question

Use numerical methods to approximate integrals and determine error estimates 1. For the following integrals, compute approximations using the left-endpoint, right-endpoint, midpoint, trapezoidal, and Simp- son methods with n = 4. Also, use the second fundamental theorem of calculus to compute the actual value and compute the absolute relative-error* for each of your approximations. * Recall that the absolute relative-error is found by computing $frac{Estimated Value - Actual Value}{Actual Value}$ × 100%. (a) $int_{t=1}^{5} (t^2 + 1) dt$ (b) $int_{t=0}^{pi} sin(t) dt$ (c) $int_{t=0}^{4} sqrt{16 - t^2} dt$

          Use numerical methods to approximate integrals and determine error
estimates
1. For the following integrals, compute approximations using the
left-endpoint, right-endpoint, midpoint, trapezoidal, and Simp-
son methods with n = 4. Also, use the second fundamental
theorem of calculus to compute the actual value and compute the
absolute relative-error* for each of your approximations.
* Recall that the absolute relative-error is found by computing
$frac{Estimated Value - Actual Value}{Actual Value}$ × 100%.
(a) $int_{t=1}^{5} (t^2 + 1) dt$
(b) $int_{t=0}^{pi} sin(t) dt$
(c) $int_{t=0}^{4} sqrt{16 - t^2} dt$

$Use numerical methods to approximate integrals and determine error estimates 1. For the following integrals, compute approximations using the left-endpoint, right-endpoint, midpoint, trapezoidal, and Simp- son methods with n = 4. Also, use the second fundamental theorem of calculus to compute the actual value and compute the absolute relative-error* for each of your approximations. * Recall that the absolute relative-error is found by computing fracEstimated Value - Actual ValueActual Value × 100%. (a) intt=1^5 (t^2 + 1) dt (b) intt=0^pi sin(t) dt (c) intt=0^4 sqrt16 - t^2 dt$

Added by Donna G.

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