Using trigonometric substitutions, S –a dx is equal to: xv16 – x²

Q: 2 I 2 Vr +25 dz

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Q: Evaluate the following using trigonometric substitution: dx V25 + x²)

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Q: If y = sin?t+ tant, x=- In(- cost) – esinr, find the value of y when t=. A ... В 2+ Vze V? D

A: Solution:

Q: Suppose that Ө is in standard position and y=9 &  r= 3 square root 13, use the given information to…

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Q: Evaluate dx 1²√√²-49) SV x>7, using a trigonometric substitution.

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Q: Use trigonometric substitution to evaluate the following dx +16

A: The following trigonometric identity is useful, while evaluating the given integral. 1+tan2θ=sec2θ

Q: Find the area inside one petal of the four-leaved rose r = sin 2x

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Q: The value of e" dx from 0.2 to 2.2 by using multiple segment trapezoidal rule, n-2 is O 7.8423 O…

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Q: S sin? (;z)d.

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Q: Calculate the area of one petal of r = sin 4θ

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Q: a) cosh (x) tanh' (?) = sech'! (?) find the "(?) " %3D %3D b) ln () = ? --

A: We are given : cosh-1(x)=tanh-1?=sech-1(?) Let,   Now, cosh-1(x)=tanh-1t=sech-1(y) Taking…

Q: Use the arc length formula, L = √√√1 + (f' (x))² dæ, to find the length of y = 2ª + 1 on [1, 5].…

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Q: Given that sin t =1/2and 0 ≤ t <π/2, find the value of cos t using a trigonometric identity.

A: sin t =12and0≤t≤π2i.e first quadrantIn 1st quadrant sin t, cos t arepositive

Q: e) With respect to y = cosx, is there a vertical stretch or compression? f) With respect to y =…

A: To answer parts e and f

Q: Evaluate the following using trigonometric substitution: dx Vx2 + 2x – 15

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Q: Find the length of the cuve, X = 5 sin t+ 5t, y= 5 cos t, 0stSA

A: Given:x=5sint+5t,   y=5cost,  0≤t≤πLength of the curve:L=∫abdxdt2+dydt2 dt

Q: 3 + In?x dx

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Q: 3. Using the fact that sin 2a = 2 sin a cos a, and the fact that 0 = 2a, rewrite the area of the…

A: As per our guidelines we can answer only 1 question so kindly repost the remaining questions…

Q: Find the area of the interior of the four-petaled rose r = sin(20)

A: The given function is fθ=r=sin(2θ). Evaluate the boundaries of the petals as follows. fθ=0sin…

Q: dx Evaluate LJv by using Trapezoidal rule (up to three 1 + x? decimal places). [Ch-4(B), Expl-2]

A: We have to evaluate ∫01 dx1+x2 by using Trapezoidal rule.

Q: cos (In x) dx

A: Given: ∫cosln xdx

Q: dx If x2 – 2x – 4 is solved by trigonometric substitution, which of the following substitutions is…

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Q: Find the length of one arch of the cycloid 8(t – sin(t)), y = 8(1 – cos(t)). %3D

A: Given: x = 8(t -sint(t)) y = 8 (1-cos(t)) To find the length of arc.

Q: 4 Tt /4 * tan*x sec*x dx

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Q: 2t k, then the distance traveled over 0Sts In 3 is:

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Q: Use this reduction formula and your answer in part a) to find ſ cosª xdx and ſ cos® xdx.

A: To find ∫ cos4 x dx and ∫ cos6 xdx First we find ∫ cos4 x dx Apply integration reduction…

Q: The value of sinh ja is equal to а. О b. -1 c. j d. 1

A: Answer

Q: ecos z sin zdz

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Q: Using trigonometric substitutions, dx is equal to: xV16 - x

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Q: Given LM tangent to OC at point L, which is an expression to represent mJK ? K a° M

A: We have the given figure as The inscribed angle theorem states that an angle θ inscribed in a…

Q: Using appropriate trigonometric substitution, dx XV9 — х2 is transformed to

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Q: Find the length of L of the Curuc R Ct) = e2* cos (E) î +e?* sin (t) ĵ +ea* 1tsin (t) ĵ teat Ŕ over…

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Q: If the area inside both the cardioid r = 6+ 6 sin 0 and the circle r = 6 is A+ B¨, then what is A+…

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Q: Using trigonometric substitution, find J Tr246rt10 dx in terms of x.

A: Hello. Since your question has multiple parts, we will solve first question  for you. If you want…

Q: y = sin x 2

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Q: Evaluate the following using the TRIGONOMETRIC SUBSTITUTION METHOD: 1.5 dx

A: Given: I=∫dxx2x2+4 For evaluating given integral, we substitute x=2tanθ…

Q: Use one of the formulas in the equation A = f. x dy = £. -ydx = } Þc x dy – y dx to calculate the…

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Q: dx after appropriate use of trigonometric substitution, it will be transformed into? Vx² –4x+1'

A: Given That: The integration, ∫dxx2-4x+1

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

A: Given inside r=14sinθ outside r=2

Q: The radius of a circle is 3 in. Find its area in terms of T.

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Q: TT secx dx cot 3x

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Q: Using trigonometric substitutions, S xv16 - 16 dx is equal to: - x2

A: Since you have asked multiple question,as per our guidelines we are supposed to answer only one…

Q: Find the area of one leaf of the "four-petaled rose" r = 5 sin 20 shown in the following figure: y…

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

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Q: Evaluate the following using trigonometric substitution: Vx2 - 4 dx

A: Find your answer below

Q: Find the length of the entire perimeter of the region inside r = 14 sin 0 but outside r = 2. Answer:

A: Given the region r=14sinθ and r=2. We need to find the length of the entire perimeter inside…

Q: Find the area inside the larger loop and outside the smaller loop of the limicon ? = 1 + 2 cos ?.

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Q: dx 9. 3/2 (4-x2)³/2

A: Given:

Q: Find the area of one leaf of the "four-petaled rose" r =7 sin 20 shown in the following figure: r=,,…

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Q: Using trigonometric substitutions, S x³/4 + x²dx is equal to:

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Ratios

A ratio is a comparison between two numbers of the same kind. It represents how many times one number contains another. It also represents how small or large one number is compared to the other.

Trigonometric Ratios

Trigonometric ratios give values of trigonometric functions. It always deals with triangles that have one angle measuring 90 degrees. These triangles are right-angled. We take the ratio of sides of these triangles.