The area enclosed by the circler= = sin 0 is given by 2x esin 0 A = f" Sr dr d0.

Q: what is the appropriate case in evaluating the given Power of Tangent and Secant in \int \tan…

A: Given:  Let I=∫tan66x sec26xdx To Find: To evaluate the given integral.

Q: Find the volume of the solid generated by rotating the Shaded region about the x-axis trigonometric…

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Q: Express the length of the curve as an integral but do not evaluate it. r = sin θ cos θ, 0 ≤ θ ≤ π

A: We have givem expression r=sinθcosθ, 0≤θ≤π We have to set up the integral for calculate the length…

Q: sinxcos 2x dx

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Q: Find the area of the region that lies inside both curves

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Q: Set up an integral that represents the length of the curve.Then use your calculator to find the…

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Q: Use an appropriate substitution and then a trigonometric substitution to evaluate the integral.…

A: By applying  trigonometric substitution

Q: Use the midpoint rule with four subdivisions to estimate ∫2 to 6 (2x2+3)dx to two decimal places.…

A: Given ∫262x2+3dx we have to use midpoint rule

Q: Find a definite integral that represents the arc length. r = 8sec(θ) on the interval 0 ≤ θ ≤ π/3

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Q: Find the integral of ∫(sin2x - cos2x)2dx. Use trigonometric transformation or integration by parts.

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Q: By iterated integration, find the area bounded by the parabola y2 = 4ax and its latus rectum, and…

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Q: . Find the area of region between two functions fix)=sinx, g(x)-cos2x,-끌sxs을 %3D

A: The area between two curves A=∫abf(x)-gxdx sinx=cos2xsinx=1-2sin2x2sin2x+sinx-1=0sinx=-1±1+84=-1,…

Q: Find the area enclosed by the curve whose equation is given below: r = 1- 0.6 sin 0

A: Given curve is r=1−0.6sinθ We have to find the area enclosed by the curve r=1−0.6sinθ Area is given…

Q: Use trigonometric techniques of integration to evaluate | tan12x sec"x dx' %3D tan15x tan13x + C II

A: To evaluate the given integral use the substitution u = tan x  and the following formula.

Q: 10 lemniscate ² = 4 cos 20 outside r = √ √√2

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Q: area bounded by the curve and perimeter when r^2=sin theta +cos theta

A: We used Octave to plot the above curve. And the code is:  theta=linspace(0,2*pi,1000);…

Q: Choose the integral that would find the area inside r = 3 sin 0 and outside r = 2- sin 0

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Q: Sketch the signed arearepresented by the intergal.Indicate the regionsof positive and negative area.

A: The given integral is,

Q: Set up an integral that represents the length of the curve.Then use your calculator to find the…

A: Consider the integral and draw the graph: From graph, we get the limits of x from 0 to 1.

Q: Find the area enclosed by the curves below from x = 0 to x = 3 y = 33 cos(3x) y = 33 sin(3x) Area =

A: Given:- y=33 sin(3x) , y=33 cos(3x)  To find:- Area enclosed by curves from x=0 to x=π/3

Q: By dividing the range into ten equal parts, evaluate TC sin x dx by Trapezoidal and Simpson's rule.…

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Q: Use the Trapezoidal Rule with n = 7  to approximate integral 0 to 20  sin (pie x) dx. Compare your…

A: The given function is fx=sinπx n=7

Q: Write expressions for the area enclosed by a curve interms of line integrals around .

A: Green's theorem transforms the line integral around C into a double integral over the region inside…

Q: 5x'/1 – x² dx

A: Given: I=∫015x31-x2dx For evaluating given integral, we substitute x=sinθ…

Q: Which integral requires more steps to find? Explain. Do not integrate. | sin° x dx OR sin°x cos x dx

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Q: dx = arcsec x + C xVx2 – 1

A:

Q: Use the Trapezoidal Rule with n = 4  to approximate integral 0 to 20  tan  (pie x) dx. Compare your…

A: ∫020tanπxdx a=0, b=20 n=4 ∆x=b-an⇒∆x=20-04⇒∆x=5

Q: Find the area bounded by y = sin²(x) and y = sin5(x) from 0 < x<

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Q: Set up an integral that represents the length of the curve.Then use your calculator to find the…

A: Given- y=sinx To find- The length of the curve on the interval 0≤x≤π. Identity Used- The length of…

Q: Use the Trapezoidal Rule with n = 7  to approximate integral 0 to 20  cos (pie x) dx. Compare your…

A: To Determine: Use the Trapezoidal Rule with n = 7  to approximate integral ∫020cosπxdx. Compare your…

Q: Find the area bounded by the curves y=sinx, y=cosx between x=0 and x=π/2. PLEASE INCLUDE HOW TO GET…

A: To find out the area bounded by the curves.

Q: What is the area under the curve y = cosx over the interval [0 ,π/2]?

A: Integrating the equation of curve in the given interval gives the area

Q: Assume a pink paint spill spreads in a circular pattern whose radius increases at a rate of 2 in/s.…

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Q: Calculate the area between the curves ² = 16 sin 20 and ²: = 16 cos 20 .Show by drawing

A: Given: The curves r2=16cos2θ , r2=16sin2θ To find: Area bounded by two curves  r2=16cos2θ ,…

Q: find the area of the limacon: r = 2 + sinx

A: To Determine: Find the area of the limacon:

Q: True or False: To evaluate the integral tan a sec" zdx, we save one sec z factor and use sec z = 1+…

A: Answer: TRUE

Q: Find the area enclosed by the curve r = 2 sin(0) + 3 sin(90).

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Q: Find the area of shaded region. sin 29 1 2 O A B.

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Q: To approximate cos(x) dx would Simpson's Rule, Midpoint Rule, or Trapezoidal Rule give a better…

A: The exact value of the given integral is 1

Q: 4 CSC* x

A: ∫csc4xco2xdx

Q: Set up an integral that represents the length of the curve.Then use your calculator to find the…

A: Differentiating with respect to x, we get Now the length of the curve is,

Q: Evaluate the definite integral that represents the area of the surface generated by revolving the cu

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Q: Find the area of the segment cut off from the curve y = sinx, 0≤x≤nt by the line y = 1/√2. HT 1/2 y…

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Q: Use the Composite Trapezoidal rule with h = approximate the improper integral 1 sin 2x dx to

A: Given,        ∫01sin2xx3dx=

Q: Use trigonometric techniques of integration to evaluate tan12x sec x dx tan15x tan13x + C

A:

Q: Use the Trapezoidal Rule with n = 10 to approximate the given integral. 20 6 cos (7x) dr Compare…

A: Given that

Q: The definite integral that calculates the area of the shaded region is given as: yA y 1

A: use the application of integral to solve for the area

Q: Find the half of the area that lies inside r =1+ sin 0 and outside r = 3 sin 0 %3D

A: Consider the given curves r=1+sinθr=3 sinθ First, find the point of intersection of the curves.…

Q: Give an example of finding an arc lenght by integral.

A: According to the given information, it is required to given an example of finding an arc length by…