1) Find the exact area bounded between the sine and cosine functions on the interval 4' 4 Clearly show your work in...
5. (12 pts.) Consider the region bounded by f(x) 4-2x and the x-axis on interval [-1, 4] Follow the steps to state the right Riemann Sum of the function f with n equal-length subintervals on [-, 4] (5 pts.) a. Xk= f(xa) (Substitute x into f and simplify.) Complete the right Riemann Sum (do not evaluate or simplify): -2 b. (1 pt.) lim R calculates NET AREA or TOTAL AREA. (Circle your choice.) Using the graph, shade the region bounded...
5. Find the exact area of each described region. a. The finite region between the curves y(y 2) and b. The region between the sine and cosine functions on the interval c. The finite region between z y - y - 2 and y 2z 1. d. The finite region between y mz and y 2- 1, where m is a positive 4' 4 constant. 6. Letfx) 12 and 2a, where a is an unknown positive real number. For what...
Show all work so that I can follow your thought process 1) Area between curves Determine the area of the region bounded by the following two functions: 2) Use the region bounded by the curves to determine the following volumes: a) Rotate the region around the x-axis b) Rotate the region aroundy 4 c) Rotate the region around the line x-1 Show all work so that I can follow your thought process 1) Area between curves Determine the area of...
Find a formula for the area of the ellipse 2) -1 by slicing vertically. Sketch the ellipse, + b2 a clearly showing a representative vertical slice. Show your Riemann sum and definite integral Recall that this is an ellipse centered at the origin with major axis length of 2a and minor axis length of 2b Note: If a b, what do you notice about your formula? Find a formula for the area of the ellipse 2) -1 by slicing vertically....
4. 5. (a) Sketch the region bounded by y- +2x-4, y-x2+4x-4 clearly indicating vertices on the graph, (b) Draw the area element AA on the graph and find a general expression for A4. (c) Set up a definite integral for A and find the area. 4. 5. (a) Sketch the region bounded by y- +2x-4, y-x2+4x-4 clearly indicating vertices on the graph, (b) Draw the area element AA on the graph and find a general expression for A4. (c) Set...
Please show full workings for both parts of the answer because I keep getting the answer wrong. Thumbs up will be given to the workings with correct answers! 7. Set up (do not solve) a definite integral that would give the area of the region under the graph of y = In x, above the x-axis, between the vertical lines x = 1 and x = e. Sketch the graph. You don't need to express with the Riemann sum definition...
cos theetha also Use Identities to find the values of the sine and cosine functions for the following angle measure. 56 e, given that cos 20 = - 65 and terminates in quadrant II sin 0 (Type an exact answer, using radicals as needed. Rationalize all denominators.) 5.5.15 Use identities to find values of the sine and cosine functions for the angle measure. , given that cos20 = -56 65 and 0° <o<90° sino = (Simplify your answer, including any...
4. [8 points] What is the volume of the solid formed by taking the the area between y = 4- 4x and the x-axis on the interval [0,1], and rotating it about x = 2? Fill in the following blanks to show your work and final answer. Setup but do not solve the definite integral. Volume of slice: Riemann Sum: Sketch of picture: Definite Integral:
Rewrite the limit of each Riemann sum as a definite integral (Show Work) Σ(2 + 3ckAXk| On the interval [0,4] melm mesh0 k-1 Rewrite the limit of each Riemann sum as a definite integral (Show Work) Σ(2 + 3ckAXk| On the interval [0,4] melm mesh0 k-1
B Consider the shaded region bounded by y=x2 – 4 and y= 3x + 6 (see above). Note that the r-axis and y-axis are not drawn to the same scale. (a) Find the coordinates of the points A, B, and C. Remember to show all work. (b) Set up but do not evaluate an integral (or integrals) in terms of r that represent(s) the area of the region. That is, your final answer should be a definite integral (or integrals)....