The graph above shows how the x-axis, the y-axis, the line y = -x + 3 and the curve %3D y = 2 sin x + 1create three bounded regions, labeled A, B, and C, in the first quadrant. Suppose region C is revolved about the x-axis. Which of the following integrals would describe the volume of the resulting solid? r2.850 Soso0 (-x+ 3)² – (2 sin x + 1)²dx r2.850 n J0,890 Sos90 (2 sin x + 1)² - (-†x+3)*dx O a fos00 (2 sin x + 1) – (-†x + 3)) *dx - 2.850 1)² - (-÷x + }'dx - 2.850 2

Q: For y = x3-7x2+15x-9 from x=1 and x=2 and above the x-axis, find the volume that results from…

A: The volume of revolution of the area under the graph y=f(x) about the y-axis between the limits x=a…

Q: Find the volume of the solid obtained by rotating the region bounded by y = 9x², x = 1, x = 5 and y…

A: If y is given as a function of x, say y = f(x); the volume of the solid obtained by rotating the…

Q: Find the exact area of the region enclosed by a = t - 9t and y = 4t/2 and the y-axis. Be sure to…

A: To Find: The area of the region enclosed by x=t2-9t and y=4t1/2 and the y-axis.

Q: Find the volume of a solid obtained by rotating the region underneath the graph of f(x) = 32 2x…

A:

Q: The base of a solid is the region in the first quadrant bounded by the line y = -1/2x + 2 and the…

A: At any point x calculate the area of cross section and integrate it over the interval.

Q: Consider the region bounded by the graph of y = 9 - x² and the y axis, between y = 1 and y = 5 in…

A:

Riemann Sum

Riemann Sums is a special type of approximation of the area under a curve by dividing it into multiple simple shapes like rectangles or trapezoids and is used in integrals when finite sums are involved. Figuring out the area of a curve is complex hence this method makes it simple. Usually, we take the help of different integration methods for this purpose. This is one of the major parts of integral calculus. 

Riemann Integral

Bernhard Riemann's integral was the first systematic description of the integral of a function on an interval in the branch of mathematics known as real analysis.