55. Prove the formula SuT-zidx=;sin using geometry by interpreting the integral as the area of part of the unit circle. x +;rv1 - x² +C

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

A:

Q: show that the rectaugle that has mancimum Qree for given PerimeTer is e sequare. in

A: Consider the provided question, We need to prove that the rectangle that has maximum area for a…

Q: evaluate the integral by completing the square and using trigonometric substitution.

A: We first complete the square

Q: Q M R 4, and MR = 8, find the area of AMPO 10, RP AMPQ, QR 1MP. If MO In 4

A:

Q: • 16. The area which is inside r r = 3-sino 5sin 0 and outside the limacon

A: According to rule of bartleby we can solve only the first question or three sub question of first…

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

A:

Q: Land. lower Find integral to8 Icu)={4. Reimann upper

A: Given: Tx=4,x∈0,2∩ℚ5,x∈0,2\ℚ Let P=x0,x1,…,xn be a partition of 0,2 Then,…

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: Find the area that is inside both r = 3 + 2cosθ and r = 3 −cosθ.

A: Area between r=f(θ) & r=g(θ) is defined as, A=12∫abf(θ)2-g(θ)2dθ

Q: Compute the area that is inside r = 3 + 3 sin and outside r = 2.

A:

Q: Which integral gines the area of the unit circle! xdyde rdrde S drdo d) dodr Q,

A: Given query is to find the integral which gives the area of unit circle.

Q: between

A:

Q: Find the area of the regi on. X = 4¢3- t2 y= t* + 2t?

A:

Q: 3. Draw the graph of the signed area represented by the integral and compute it using geometry. |…

A:

Q: Find the area in the first quandrant bound by the parabola y

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

A: We have to find the integral

Q: Find the area inside r=1+sin θ and outside r=3sin θ.

A: Concept: The calculus helps in understanding the changes between values that are related by 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: ;: The integral that represents the length of the arc of the curve y? = x' between the points (1, 3)…

A: It's true

Q: SKetch the 24+3x=7 enclosed by 2y= 4/x, 3, and %3D %3D regan Decige whether tjintegrate with respect…

A: area between the curves = ∫(upper curve - lower curve)dx Or∫(upper curve-lower curve)dy

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

A: Solution:-

Q: If NS = 16, find the area of O MNOP. N 10 6. R 8 S 3 T

A: Given: NS= 16 MR=10 RS = 8 OV= 9 ST=3 The Area of the region MNOP is determined as: MNOP=Area…

Q: 5.Find the area Hhat is incide r=4 and autside rz 4-2sin &

A: To find the area that is inside the r=4 and outside r=4-2sinθ r=4 and r=4-2sinθ…

Q: Find the area enclosed by r = 2 sin 30.

A:

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

A:

Q: • S/2 csc²2x√√1+cot 2x dx TT/8

A: The given integral is∫π8π4csc22x1+cot2xdx. The objective is to solve ∫π8π4csc22x1+cot2xdx.

Q: Y 36 in 23 in W V U

A:

Q: the iner tind the area bound and the y-axir in the Firt quadrant.

A:

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

A: The diagrammatic representation is,

Q: 1. Find the area enclosed between the graphs of y = 5 – 10x + 7x? – a3 and y = 4x – 3.

A: given equations are

Q: In AMPQ, QR IMP. If MQ = 10, RP = 4, and MR = 8, find the area of AMPQ.

A: Given that In ∆MPQ, QR is perpendicular to MP and also we have MQ=10,RP=4 and MR=8.Our Aim is to…

Q: Find the area enclosed by r² = 4 sin 20.

A:

Q: 11) 33.6 in 16.8 in

A: Since you have asked multiple questions in a single request so we will be answering only first…

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

A:

Q: Of the expressions w could be correctly I to compute the area ded by graph Y=10x- and line y=2x ?

A: Please refer to the image below

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

A:

Q: Calculate the area enclosed by r = 6 cos(3 0) for а) 67 b) О 2л 37 97 97 2

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: Compute the indicated integral by findng the area of the trapezoidal figure below. 110 4,0 F1 10 •5…

A: Given: A=∫35x+3dx

Q: 16.7. Use Green's Theorem to show that Area of D zdz.

A:

Q: Find the area between y = In x and the x-axis from x = 1 to x = 3. * 3 In 3 - 3 In 3 3 In 3 + (-2)…

A:

Q: Find the area of the reglon outslde r=5+5sin8, but Inside r= 15 sin 8.

A: We will solve the problem

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

A:

Q: Evaluate the integrals by making a substitution(possibly trigonometric) and then applying a…

A: Given: The integral is ∫(r2-1)3/2rdr   Reduction formula: ∫tann(x)dx=tann-1(x)n-1-∫tann-2(x)dx