Consider the region bounded by the y-axis, y = 12,  and  y = 1 + 8x3/2. (a) Write, but do not evaluate, an integral equation that will find the value of k so that  x = k  divides the region into two parts of equal area. (Round your answer for the upper limit of the integral to two decimal places.)   (c) The region is the base of a solid. For this solid, the cross sections perpendicular to the x-axis are rectangles with a height of 3 times that of its width. Find the volume of this solid. (Round your answer to three decimal places.)

Q: 1

A: The given curve is:y=x3The interval is given as:x∈[0,4] It is required to find the surface area of…

Q: 37 (a) Find the area of the region enclosed by the parabola y = 2x - x² and the x-axis. (b) Find the…

A:

Q: 1. Find the intersections between the curve y=√√3-x and line y+1-x=0 (a) Sketch the region R bounded…

A:

Q: 6. (a) Carefully sketch (and shade) the (finite) region R in the first quadrant which is bounded…

A:

Q: (2) Find the area of the region bounded by the parabolas: y = x² and y = Include a sketch in your…

A:

Q: Find the volume of the solid above the triangle with vertices (0, 0), (-1, 0) and (-1, 2), below the…

A: Given The triangle with vertices 0,0, -1,0, -1,2,below the surface z=sinπx2

Q: Find the area of R

A:

Q: x=√4−y, y=0, and y=x+2. a. Sketch the region enclosed by the curves.  b. Find the area of the…

A:

Q: Find the area of the region bounded by the hyperbola 25x2 - 4y2 = 100 and the line x = 3.

A: We have to find the area of the region bounded by the hyperbola 25x^2-4y^2=100 and x=3 Please see…

Q: (6) (2x+3y) cm Diagram 18 shows a trapezium. Calculate the area, in cm², of the trupezium. 10x cm…

A:

Q: If V=R\power{3}, and W\index{1} is the xy plane and  let W\index{2} is yz-plane:…

A: Let (a,b,c) be any element of R3, then (a,b,c)=(x,y,0)+(0,y,z)=(x,2y,z) ⇒a=x, b=2y, c=z ⇒a,b,c∈R ⇒…