Directions: Give the answer completely. Show the graph and the plane region in the Cartesian plane. 1. Find the area of the plane region with the following conditions: A. bounded by the curves y = 2x - 1 and y=-x²+x+3 B. bounded by the curves y = sinx and y = cos x, and the lines x = 0, and x = F 2. Set up definite integral of the area of the region bounded by the curves x = -y² +4 and y=x-2.

Q: Which of the following regions have the same area? I. The region enclosed by the curve y = |x2 − 1|,…

A: Part (1):- Given curves are  y=x2-1,  the lines x =0 and x=2 and the x-axis. Area = ∫01 -x2-1dx +∫12…

Q: Q1.A: Find the area of the shaded region shown in figure (1). y = 1 y = x2 x 1+ y2 Figure (1) y = -1

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Q: Let R be region above y = 1, between x = 0 and y = // (a) Sketch R. Label all curves and…

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Q: The graph of the derivative f'(x) of f(x) is shown. Compute the total change of f(x) over the given…

A: Graph of f'(x) vs x is given. Here, f'(x)=∆f∆x Therefore, change in f(x) will be, ∆f=f'(x)·∆x It…

Q: (a) Draw a sketch of the graph. (b) Determine the boundaries. (c) Find the area. 1. y = x2 – 2x and…

A: Let's find.