Use appropriate formulas from geometry to evaluate the integral dx. Write the exact answer. Do not Answer

Q: Find the area of the interior of the four-petaled rose r=sin(2θ)

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Q: Evaluate the integral. 15e cos(2x) dx +C NOTE: Enter the exact answer.

A: This question is based on indefinite integral.

Q: Evaluate the integral / (4e* + 7 cos a) dæ. Answer

A: Given that: ∫05(4ex+7cosx)dx

Q: After choosing the appropriate trigonometric substitution the integral dx, becomes

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Q: ALMN, S is the centroid. If SQ=22 find LS.

A: Here we have been given the measurement of SQ = 22 and S is the centroid.

Q: Evaluate each integral using GEOMETRY. Draw a picture, and show your work. a. (2x-4)dx SV4-x'dx b.

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Q: Evaluate the integral. | 17e3 cos(2x) dx + C NOTE: Enter the exact answer.

A: SOLUTION-

Q: Sketch and evaluate the reverse in tegral 9/x dy dz

A: Consider the provided integral,

Q: use the disTance Formula to Find the distonce between (e)and(3,2)

A: We use the distance formula to answer the given question.

Q: The area common to the circle > = 3 and the cardioid r = 3(1 - cos 9).

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Q: a) Ś ingro find the value of the i od specify the integrel caiedes |-x2

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Q: dx Use integral tables to evaluate (Type an exact answer, using radicals as needed.) xV23 + x?…

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Q: S dy 2 2 +1

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Q: Evaluate the integral. 15e* sin x d +C NOTE: Enter the exact answer.

A: We have to find the integration .

Q: ーx? + 4x +5 dx. Consider Using trigonometric substitution, what is the integral form in terms of

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Q: Use integration and trigonometric substitution to find the area enclosed by the ellipse: + = 1. 9 36

A: Given ellipse:-             x29+y236=1 =>      x232+y262=1  compare to standard form x2a2+y2b2=1…

Q: Find the integral by trigonometric substitution: ∫√1-7w^2 dw

A: The given integral is ∫ 1-7w2 dw. Substitute w=17sinx   and   dw=17cosx dx in the above integral and…

Q: Evaluate the integral o dz where C is the circle |2| = 2. 22 + 9

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Q: Find the integral: J 3sinhæ-5cosha da Select one: a. -글arccos를 + C b. 글arcsec를 +C c. 글aresin를 +C…

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Q: Evaluate the integral. cot (2x) csc°(2x) dx = + C NOTE: Enter the exact answer.

A: The given integral is ∫cot32xcsc32xdx

Q: Use a computer algebra system to approximate the iterated integral. 2/2x (x + 4y) dy dx J.2 Viewing…

A: The given integral is (x3+4y3) limit of y from x2 to 2x and limit of x from 0 to 2.

Q: S sec³p tan p dp

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Q: Evaluate the integral (Trigonometric Substitution) 1 (b²y6 – y®)Zdy

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Q: dydx, where D is the circular region inside the unit circle

A: We are given the integral,                     . Let us convert the above integral into the polar…

Q: After choosing the appropriate trigonometric substitution the integral 4 x dx, becomes

A: Apply trigonometry property and solve it

Q: a. Use integrals to show that the circumference of the circle x2 + y? a? is 2na. %3D b. Find the…

A: Solving question (a),

Q: x2 dx J V4x – x²

A: Given:       ∫x24x-x2dx    =∫x24-x-22dx  substitute u=x-2→dudx=1→dx=du                    use…

Q: To evaluate dx using trigonometric substitution, which of the following is the new integral form in…

A: Given integral is ∫x2-x2-1 dx.

Q: Evaluate the integral using appropriate substitution. an NOTE: Enter the exact answer. sin (80) d0…

A: The given integration,θ    ∫sin38θ dθ

Q: Evaluate the integral. |1° In(a) dæ =[ NOTE: Enter the exact answer.

A: Using integration by parts rule

Q: The center of Dis R. Rare}

A: As the centre of group D4 is {R0,R180}•

Q: For each integral, state which trigonometric substitution you would use to integrate by…

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Q: dx Evaluate the integral / by completing the square and using trigonometric substitution x² + 4x +…

A: Solve the following integral

Q: Write, but do not integrate, an integral expression that will calculate the circumfrence of the…

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Q: QLewalnate the following integrats Sin?xcos"xdx

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Q: Sin X' cOS X dxN 9x2 16-x3 dx

A: 1. Given integral is ∫π4π3sinx·cosx dx Substituting  sinx=u ⇒cosx dx=du Hence, limits becomes,…

Q: If the integral contains v(x^2 - a^2), the best trigonometric substitution to be used is A. let x =…

A: Solution is written in below steps.

Q: Use a familiar formula from geometry to find the length of the curve described and then confirm…

A: Recall:  L=∫abr(θ)2+r'(θ)2dθ We have, r=7sinθ+2cosθ, a=0, b=π

Q: a) cosh (x) tanh' (?) = sechi! (?) find the "(?) In 1- i

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Q: After choosing the appropriate trigonometric substitution the integral | x2 - dx, becomes

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Q: Sin 2 x cos xdX =? Xdx =? %3D X COS KINC

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Q: Evaluate the integral by making exactly one u-substitution and applying any necessary formula(s)…

A: Solution..

Q: ,3 Y = 0 < x < 2 9

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Q: Evaluate the integral by completing the square and applying appropriate formulas from geometry.…

A: Topic = Integration

Q: Jse the arc length formula to find the length of the line segment y = 3- 2x, 0sxs2. The length of…

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Q: SSJityt 16xy dA. D

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Q: Watch the video on a u-substitution followed by a this question. To start the integral a V1+x6 dx,…

A: Given problem is : Solution : We use substitution to simplify the integral.

Q: Use an appropriate trigonometric substitution to evaluate the following definite integral 1 2+1 da.…

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Q: Evaluate the integral (Trigonometric Substitution) |(a?x* – x®)&dx 6. x³)Zdx

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Cylinders

A cylinder is a three-dimensional solid shape with two parallel and congruent circular bases, joined by a curved surface at a fixed distance. A cylinder has an infinite curvilinear surface.

Cones

A cone is a three-dimensional solid shape having a flat base and a pointed edge at the top. The flat base of the cone tapers smoothly to form the pointed edge known as the apex. The flat base of the cone can either be circular or elliptical. A cone is drawn by joining the apex to all points on the base, using segments, lines, or half-lines, provided that the apex and the base both are in different planes.