4. a. Draw a region R bounded by the curves y = x² +4 and y=x+2, then detemine its area. b. Find the volume if the area Rin problem 4a is rotated around the x-axis.

Q: 2. Find the area enclosed by the line x = y+ 1 and the parabola y - 2x + 6. All answers must be in…

A: The given problem is to find the area enclosed by the given line x=y+1 and the parabola y2=2x+6.

Q: 1. Find the area between y intersection points. = 3x²+2x+1 and y = 7x+2. Use technology to find the

A: Area = 4.1678 square unitsExplanation:Given curves:y=3x2+2x+1y=7x+2 The curves can be plotted as…

Q: Find the of the region bounded by the parabolas y – 6x = -x² and y + 2x = x² , area

A:

Q: 6. Find the area enclosed by the curve x² + 8y + 16 = 0 the x-axis, the y- axis and the x-4 = 0…

A:

Q: Find the volume of the area bounded by the line y = 3x + 4 and the curve y = x² if it is revolved…

A:

Q: Find the AREA and VOLUME (Identify what type of volume) bounded by the equations; y = 4x - x² and x…

A: The given curves are y=4x-x2 and x+y=4 We have to find the area and the volume bounded by these…

Q: B) Find the area of the region enclosed by the Parabola y = 2 – x2 and the line y + x = 0 ?

A: The region is bounded by y=2-x2 and y+x=0

Q: 2. Find the volume if the area bounded by the curve y = x³ +1, the x-axis and the limits of x=0 and…

A: Given curve is y=x3+1, the x-axis and the limits are x=0 and x=3. The objective is to find the…

Q: Find the area of the region enclosed by the line y=4x and the curve y= x+ 3x.

A:

Q: Use inscribed and circumscribed rectangles to find the area of the region to the right of the line x…

A: Concept: the area between the region y=f(x) and ==g(x) on the interval [a, b] Let us assume that…

Q: 1. Find the total area bounded by the curves y=x²-3x and y = x³ + x² −12x.

A: Given curves are y=x2-3x y=x3+x2-12x Take  y=fxHere,   fx=x2-3x y=gxHere,   gx= x3+x2-12x

Q: 1.) Find the area of the region bounded by the parabola y = 2x and the line y = x - 4

A:

Q: 1. Find the area between y = - x² + 4x and y = x² - 6x + 5. Graph and shade the area required.

A: