Approximating definite integrals with a calculator Consider the following definite integrals. a. Write the left and right Riemann sums in sigma notation for an arbitrary value of n. b. Evaluate each sum using a calculator with n = 20, 50, and 100. Use these values to estimate the value of the integral. 70. ∫ 4 9 3 x d x
Approximating definite integrals with a calculator Consider the following definite integrals. a. Write the left and right Riemann sums in sigma notation for an arbitrary value of n. b. Evaluate each sum using a calculator with n = 20, 50, and 100. Use these values to estimate the value of the integral. 70. ∫ 4 9 3 x d x
Approximating definite integrals with a calculator Consider the following definite integrals.
a. Write the left and right Riemann sums in sigma notation for an arbitrary value of n.
b. Evaluate each sum using a calculator with n = 20, 50, and 100. Use these values to estimate the value of the integral.
70.
∫
4
9
3
x
d
x
With differentiation, one of the major concepts of calculus. Integration involves the calculation of an integral, which is useful to find many quantities such as areas, volumes, and displacement.
c. Evaluate the indefinite integrals by selecting an appropriate substitution. Remember to change the bounds for indefinite integrals. Solve c) i.
c. Evaluate the indefinite integrals by selecting an appropriate substitution. Remember to change the bounds for indefinite integrals. Solve c) iv. The question asks to evaluate the indefinite integral.
For the function, do the following.
f(x) = 2x from a = 3 to b = 4
(a)
Approximate the area under the curve from a to b by calculating a Riemann sum using 5 rectangles. Use the method described in this example, rounding to three decimal places.
______square units
(b)
Find the exact area under the curve from a to b by evaluating an appropriate definite integral using the Fundamental Theorem.
_____________ square units
Chapter 5 Solutions
MyLab Math with Pearson eText -- Standalone Access Card -- for Calculus: Early Transcendentals (3rd Edition)
Precalculus Enhanced with Graphing Utilities (7th Edition)
Precalculus Enhanced with Graphing Utilities
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.
Definite Integral Calculus Examples, Integration - Basic Introduction, Practice Problems; Author: The Organic Chemistry Tutor;https://www.youtube.com/watch?v=rCWOdfQ3cwQ;License: Standard YouTube License, CC-BY