Please answer the question on the image and please give full explanation to the answer. Let R be the finite plane region trapped between the curves y = vx and y =x².Sketch R and express| sin(cos(In x)) dAas an iterated integral.(Do not evaluate the integral; just set it up.)

Name: Please answer the question on the image and please give full explanati
Uploaded: 2024-03-20T07:07:37.000Z
Channel: Bartleby
Description: Please answer the question on the image and please give full explanation to the answer. Let R be the finite plane region trapped between the curves y = vx and y =x².Sketch R and express| sin(cos(In x)) dAas an iterated integral.(Do not evaluate the i

Given R is the region in between the curves, y=x and y=12x2. To plot the graph, consider the table below, Table values of y=x, x 0 1 4 y 0 1 2 Table value of y=12x2 x 0 ±1 ±2 y 0 12 2 Therefore, the required graph is, Here, the shaded region is R.To find the point of intersection of these curves. x=12x2x2x=2x3=4x=1.587 Therefore, y=1.26. So, the point of intersection of these curves is 1.587, 1.26. From the region, R sketched above, x varies from 0 to 1.587 and y varies from y=12x2 to y=x. Therefore, the given integral becomes, ∬Rsincosln xdA=∫01.587∫12x2xsincosln xdydx.