The following function is positive and negative on the given interval.元f(x) = sin 2x; म4a. Sketch the function on the given interval.b. Approximate the net area bounded by the graph of f and the x-axis on the interval using a left, right, and midpoint Riemann sum with n=4.c. Use the sketch in part (a) to show which intervals ofmake positive and negative contributions to the net area.

Answered: The following function is positive and…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Find the left end approximation for the area between the curve and the x-axis on the interval [0, 2] with n = 4 for the function f (x) = -x4 – 3x?. What do you think will be the actual area between the curve and the x-axis on the interval 0, 2 with n = 4 for the function f (x) = -x4 – 3x2. Evaluate the definite integral f (csc² 0 – cos 0) do. I
The following function is positive and negative on the given interval f(x)=sin 2x a. Sketch the function on the given interval b. Approximate the net area bounded by the graph off and the x-axis on the interval using a left, right, and midpoint Riemann sum with 4 c. Use the sketch in part (a) to show which intervals of make positive and negative contributions to the net area a. Choose the correct answer below. OA. 241 1- 0- HO Aly ER Q Q C 7x of [7] OA. Positive on c. Which intervals of x- OB. Positive on b. Use a calculator to approximate the area. The net area, approximated using the left Riemann sum with n=4 is (Do not round until the final answer. Then round to three decimal places as needed) OC. Positive on x, Use a calculator to approximate the area. The net area, approximated using the right Riemann sum with n4.i (Do not round until the final answer. Then round to three decimal places as needed) [0,x); negative on [x.2x) 3x 7x 214 - Use a calculator to approximate the area. The…
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a. Approximate the value of the integral by using rectangles. For your approximation use right endpoints and let n = 4 b. Evaluate the integral by interpreting it in terms of areas. Draw a picture c. Evaluate the integral using the Fundamental Theorem of Calculus Part 2 FTC2)
dr A remarkable integral It is a fact that Jo 1+ tan" x /2 =7. for all real numbers m. a. Graph the integrand for m = -2, –3/2, –1, –1/2, 0, 1/2, 1, 3/2, and 2, and explain geometrically how the area under the curve on the interval [0, 7/2] remains constant as m varies. b. Use a computer algebra system to confirm that the integral is constant for all m.

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