(a) Explanation Given information: The curve function is y = x 2 . The interval is 0 ≤ x ≤ 2 . Revolution about x axis: If the function f ( x ) ≥ 0 is continuously differentiable on [ a , b ] the area of the surface generated by revolving the graph of y = f ( x ) about the x axis is S = ∫ a b 2 π y 1 + ( d y d x ) 2 d x Calculation: Show the curve Equation as follows: y = x 2 (1) Differentiate Equation (1) with respect to x . d y d x = d d x ( x 2 ) = 2 x Take square on both sides (b) To determine Sketch the graph for the function y = x 2 . (c) To determine Calculate the surface area numerically by using integral evaluator.

Thomas' Calculus: Early Transcendentals Plus Mymathlab With Pearson Etext -- Access Card Package (14th Edition) (hass, Heil & Weir, Thomas' Calculus Series)

14th Edition

ISBN: 9780134665573

Author: Joel R. Hass, Christopher D. Heil, Maurice D. Weir

Publisher: PEARSON

See similar textbooks

Concept explainers

Numerical Integration

In a mathematical investigation, numerical integration comprises a wide group of calculations for computing the mathematical estimation of definite integral, and likewise, the term is moreover in some cases used to depict the numerical solution of differ…

Videos

Question

Chapter 6.4, Problem 2E

(a)

To determine

Form an integral for the surface area generated by revolving the curve about x axis.

(b)

To determine

Sketch the graph for the function y=x2.

(c)

To determine

Calculate the surface area numerically by using integral evaluator.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 6.4, Problem 1E

Chapter 6.4, Problem 3E

Students have asked these similar questions

Under certain conditions, the number of diseased cells N(t) at time t increases at a rate N'(t) = Aekt, where A is the rate of increase at time 0 (in cells per day) and k is a constant. (a) Suppose A = 60, and at 3 days, the cells are growing at a rate of 180 per day. Find a formula for the number of cells after t days, given that 200 cells are present at t = 0. (b) Use your answer from part (a) to find the number of cells present after 8 days. (a) Find a formula for the number of cells, N(t), after t days. N(t) = (Round any numbers in exponents to five decimal places. Round all other numbers to the nearest tenth.)

The marginal revenue (in thousands of dollars) from the sale of x handheld gaming devices is given by the following function. R'(x) = 4x (x² +26,000) 2 3 (a) Find the total revenue function if the revenue from 125 devices is $17,939. (b) How many devices must be sold for a revenue of at least $50,000? (a) The total revenue function is R(x) = (Round to the nearest integer as needed.) given that the revenue from 125 devices is $17,939.

Use substitution to find the indefinite integral. S 2u √u-4 -du Describe the most appropriate substitution case and the values of u and du. Select the correct choice below and fill in the answer boxes within your choice. A. Substitute u for the quantity in the numerator. Let v = , so that dv = ( ) du. B. Substitute u for the quantity under the root. Let v = u-4, so that dv = (1) du. C. Substitute u for the quantity in the denominator. Let v = Use the substitution to evaluate the integral. so that dv= ' ( du. 2u -du= √√u-4

Chapter 6 Solutions

Thomas' Calculus: Early Transcendentals Plus Mymathlab With Pearson Etext -- Access Card Package (14th Edition) (hass, Heil & Weir, Thomas' Calculus Series)

Knowledge Booster

$Calculus$

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.