Consider the following. -aR- *br (a) Set up an integral for the volume a solid torus (the donut-shaped solid shown in the figure) with radii br and aR. (Let a = 5 and b = 3 3r dy (b) By interpreting the integral as an area, find the volume V of the torus. V =

Q: Find the total area between r = 4 sin(0) and r = 7 sin(40). %3D

A: Double integral is used to integrate the function of two variables over two-dimensional region.…

Q: The lateral area L of any prism whose altitude measures h and whose base has perimeter P is given by…

A:

Q: Find the area bounded by the ff. curves and lines: a. arch of y =(1/3)sin(x/3)

A: Consider  the equation

Q: r=5+4sin(theta), r=5+4cos(theta) Find the area if the region that lies inside both curves

A:

Q: the Area under tro choid one arch of the ( = 70-1sine. 1Sine, y= 1cose

A:

Q: b) Heron's Formula states Area = √5(5-a)(s-b)(s-c), where s = 1/(a+b+c) prove using the following…

A:

Q: Find the area of the region inside one leaf of the five​-leaved rose r=4cos5θ

A: Given: r = 4cos(5θ)

Q: Is it possible to get the area between y2 = 3x and y = x³, using a. vertical strips b. horizontal…

A: We have to find area under the curves.

Q: Sketch the curves y = 3x and y = x and determine the area enclosed by them.

A: we can find the area enclosed by the curve by setting up the double integral. to find the limit of…

Q: = = Ca R be the shaded region in closed by the graphs of ex²-1, and the y-ax igure at right. culator…

A: y=ex-1y-1+sinx

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.