4) Show that the circumference of the unit circle is equal to 1 1 dæ (an improper integral) x2 Evaluate, thus verifying that the circumference is 27.

Q: Find the length of the entire perimeter of the region inside 15 sin 0 but outside r = 1.

A: The region is inside r=15sin θ but outside the r = 1

Q: а. Find the integral of e42 dz, where C is a circle z-2= 8 and x 1+ last digit of your ID.

A: In the given question we have to calculate the integral I=∮Ce4z(z-x)6dz where C is circle z-2=8 and…

Q: Evaluate the integral (2.x - y)dA, where D is the region in the first quadrant enclosed by the lines…

A:

Q: The area of a circle with center origin and radius r is described by the following integral: O A. O…

A:

Q: Evaluate the given integral where C is the left half of the unit circle in ccd.

A: Note:- In given problem you mention "ccd" but one short form has different different full form. So,…

Q: Given that ex dx = e3 - e, use the properties of integrals and this result to evaluate (4ex – 2) dx.

A:

Q: Use the form of the definition of the integral given in the theorem to evaluate the integral. La (12…

A: According to the given information, it is required to evaluate the integral.

Q: Use a computer algebra system to evaluate theintegral. Compare the answer with the result of using…

A: Given integral is

Q: Evaluate the integral by interpreting it in terms of area. 4 V16 – x dx

A:

Q: 2- Find the area f the negion cut from the trst quadrant by the regson r= l+ Sino?

A: From the given problem:   r=1+sinθ   Given first quadrant it means:   θ→0 to π2r→0 to 1+sinθ   Now…

Q: Find the area of the region outside r = 7+ 7 sin 0 , but inside r = 21 sin 0. Preview

A: Given Data The outside function is r=7+7 sin θ. The inside function is r=21 sin θ.   Equate the…

Q: Evaluate the integral. Sacot*x ox 4 cot x dx =

A: We have to find the integral

Q: Evaluate the integral. sech?x +C. 4 + tanh x

A:

Q: evaluate the integral using the methods covered in the text so far.

A:

Q: Use Simpson's rule with n = 18 to calculate the circle's area, which is specified overhead by f(x) =…

A: Given: The circle, which is specified overhead by fx=3-x2 and beneath by gx=-3-x2.   To calculate:…

Q: Estimate the, area undex fle) = SinCo) between = o x= n Using the sigkect end point rectan gles h to…

A:

Q: An area bounded byy = 0, x = 0, and y = e*, is revolved about the x-axis. 7. CD method is…

A: Yes it is true we can use CD method here for area revolution and find volume generated due to area…

Q: vn to the right. What is the total weight of the 16 24 De 13 14 tices given above into the area…

A: In this question, Nearest Neighbor Method is applied. Nearest Neighbor Method The idea behind…

Q: ;: The integral that represents the length of the arc of the curve y? = x' between the points (1, 3)…

A: It's true

Q: Find the area. Sin 9in BD = 6in B. A,

A: Use formula of area of triangle

Q: Show that if k is a positive constant, then the area between the x-axis and one arch of the curve y…

A: y = sin kx cuts the x axis at y=0. Solve for x.

Q: Find the integral giving the area of the region in Quadrant II that is inside r=1/2 and outside…

A:

Q: 2 y = | (x 3. 4x + 5) dx

A:

Q: Find the area pebal r=4 sin C30) of one

A: Let's now plot the graph:

Q: (241) dz (24)(러3)(2)

A: Solution:

Q: Evaluate the double integral : 4 3, 3x Si Si +14) dy dæ Answer:

A: Using integration formula we can solve this double integral

Q: Without using symmetry, determine a definite integral that reprresents the area of the region…

A: Sketch polar coordinates system and convert r in term of theta

Q: find the area enclosed by one loof of the curve of r = sin(4θ)

A:

Q: Evaluate the integral 1 1-x x dzdydx. x2 Jo

A:

Q: 3- Find the area of regida common to the Car diaids and rzて |- Cose?

A:

Q: The integral (ydx - xdy) is evaluated along the circle x² + y² - traversed in counter clockwise…

A:

Q: (b) By reffering to Figure 2, give an integral equal to each area. y A y = 2.x y = x² 4, A, х Figure…

A: Given

Q: Using iterated integrals, find the smaller area cut form the circle x² + y2 = 16 and the line y =-1.

A: to find the area we consider th strip parallel to y axis  and desctribed the region as below

Q: find the area of the circle r=a by integration

A: The diagrammatic representation is,

Q: 2. (a) Find the area of a region that lies inside the circle r = 2 sin 0 and outside the circler 1.

A:

Q: the Area that lies inside r=3+2 sin 0 out side r=2 is -23.957 O -24.187 O 23.957 O 24.315 O 24.187 O…

A: We have r=3+2sinθ  , r=2 We find the point of intersection: 3+2sinθ=2⇒sinθ=-12⇒θ=sin-1-12⇒θ=7π6,…

Q: Find the area that enclosed by the circle r-2sin 0 for 4 ≤ 0 ≤T/2 | (+-#) V=2sin o ty

A:

Q: Find the area between the paral x = y? – 1 and x = 2y? – 2

A:

Q: 25. Show that the circumference of the unit circle is equal to dx (an improper integral) 2 Evaluate,…

A:

Q: Find the value of the integral of g(z) around the circle |z – i| =2 in the positive sense when g(2)…

A:

Q: 55. Prove the formula SuT-zidx=;sin using geometry by interpreting the integral as the area of part…

A: We have given the integral;

Q: The value of the integral dz, over the Contour C |2- 2| = 2 is equal :- 2

A: Cauchy's integral function: Suppose C is a simple closed curve and the function f(z) is analytic on…

Q: 5. Find the total area betweenr = 4 sin(0) andr = 7 sin(40). %3D %3D

A:

Q: 2. Find the length of the entire perimeter of the region inside r = 14 sin 0 but outside r = %3D…

A:

Q: Consider the area between the graphs x + 2y = 29 and x + 6 = y?. This area can be computed in two…

A:

Q: Find the area that it encloses. r = 2 − 2 sin(?)

A: To find: The area that encloses r = 2 − 2 sin(?). Graph: The polar curve  over the interval [0,2pi]…