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- Consider the region bounded by the graphs of y = ln x, y = ex, x = 1, and x = e. Set up the definite integral that solves for the volume of the solid when the region is revolved about:a. the x-axis b. the y-axis c. the line x = -1 d. the line y = -1arrow_forwardy = ex , y = 0 , x = 0 , x= ln2 Draw the region bounded by the curves y = e^x , y = 0 , x = 0 , x= ln2 in the first quartile. Express the area of this region as a double integral. Solve the integral.arrow_forwardGiven the two functions y=x^3 and y=x Find the area between the two functions y=x^3 and y=x bounded between the lines x=0 and x=2. A. Draw a picture and shade the two areas with two different colors. Mark clearly the vertical boundaries. Show any intersection points between y=x^3 and y=x on [0,2]. B. Show the complete integral set up: You will need to show two seperate integrals. C. Evaluate both integrals using technology. My answer for the area between the two curves y=x^3 and y=x on [0,2] is: _______________arrow_forward
- A solid S is generated by revolving the region between the x-axis and the curve y =√ sinx (0 ≤ x ≤ π) about the x-axis.(a) For x between 0 and π, the crosssectional area of S perpendicular to the xaxis at x is A(x) = _____.(b) An integral expression for the volume of S is _____ .(c) The value of the integral in part (b) is_____ .arrow_forwardConsider the integral shown below: π ∫ (ln(x))/((x^2)−2x+2) dx. 1 Evaluate the integral using: Romberg Integration to find R(3,3). Show all work, Gaussian Quadrature with two nodes, Gaussian Quadrature with three nodes,arrow_forwardSetp up and do not evaluate the integral for the region's volume when R is revolved about the line y = 1, usingthe method of washers.arrow_forward
- a. Poses without evaluating an iterated integral to evaluate ( , ) R f x y dA , where 2 3 f x y x y ( , ) 1 = + , & R is the region bounded by curves and x and x = = = 2 , 0, 5 . b. Evaluate the above integral to find a numerical result. c. Set up a multiple integral to evaluate the volume of the solid bounded by the curves: x = 4 – y two , x = y two , z = 0, z = 3. d. Evaluate the above to find a numerical resultarrow_forward34) The figure shows the region of integration for the integral. Rewrite this itegral as an equivalent iterated integral in the five other orders. ∫0 to 1 ∫0 to (1-x^2) ∫0 to (1-x) f(x, y, z) dydzdxarrow_forward4. Evaluate the double integral over rectangle S, xycosy dA, R:[-1,2] x [0, Pi]arrow_forward
- The region R is bounded by the curve y = ln x and the x-axis on the interval [1, e]. Find the volume of the solid that is generated when R is revolved in the following ways. 1 About the line x = 1 2 About the line y = 1.arrow_forwardA triple integral Use a change of variables to evaluate ∫∫∫D xz dV, whereD is a parallelepiped bounded by the planesy = x, y = x + 2, z = x, z = x + 3, z = 0, and z = 4arrow_forwardEvaluate the double integral for the function f(x, y) and the given region R. (Give your answer correct to 3 decimal places.) f(x, y) = 4xy3; R is the rectangle defined by 3 ≤ x ≤ 4 and −1 ≤ y ≤ 0arrow_forward
- Calculus: Early TranscendentalsCalculusISBN:9781285741550Author:James StewartPublisher:Cengage LearningThomas' Calculus (14th Edition)CalculusISBN:9780134438986Author:Joel R. Hass, Christopher E. Heil, Maurice D. WeirPublisher:PEARSONCalculus: Early Transcendentals (3rd Edition)CalculusISBN:9780134763644Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric SchulzPublisher:PEARSON
- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning