Integrate the equation using the method in trigonometric substition

Q: Given the integral secº (x - 1) tan* (x − 1)dx, which of the following equations will be useful for…

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Q: x+2 Determine the case of the following proper rational function after simplification: (x2 -…

A: Here, the rational function is: x+2(x2-4)(x3-8)=x+2(x2-22)(x3-23)=x+2(x-2)(x+2)(x-2)(x2+2x+4)

Q: must

A: When a curve changes from concave down to concave up or concave up to concave down , that means…

Q: The orthogonal trajectories of the family of curves y = cx² is A x=ky² B C x²+2y²=k 2x² + y² = k

A: We have to find the

Q: S. S. (x + 2y)dydx = 10, Jo a

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Q: Find the volume of solid generated by revolving the region bounded by f(x) = x² + 1and…

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Q: dx Transforming secx + 1 2-2z² A 1+z² ® √ ₁ + 2²/1d² +z² B -dz 1-z² z²+z C / 1-z² Ⓒ / 1-²/²0 D 1+z²…

A: To find the transformation of the integral ∫dxsec x+1 after using miscellaneous substitution.

Q: * The evaluation of So So x y ex² dxdy is 0.25 e - 0.5 0.25 e - 0.25 None of them

A: The objective is to evaluate the double integral.

Q: SHOW COMPLETE SOLUTION (NO SHORTCUTS PLEASE) (Differential Equations) Find the general solution of…

A: Let's solve given diffrential equation.

Q: d If g(x)=- -S*[e' - In (21+1)]dt, find g(x) Se dx 4 A (2x+1)² 4 B e+ (2x + 1)² Ⓒe* -In (2x+1) 2 D…

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Q: the equation of the tangent line to the curve y = 4 sin x at the point equation of this tangent line…

A: We are asked to find the tangent line of the curve.

Q: Which of the following represents the volume of the solid generated by revolving the region bounded…

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Q: y=Arccos (x²)

A: The objective of the question is evaluate the second derivative of the given function.

Q: d²y If x=5+ cos20 and y=3- sin20, what is ? dx² A csc ³20 (в B - cot20 Ⓒ-csc ³20 D cot20

A: Given: x=5+cos2θ and y=3-sin2θ Now, dxdθ=d5+cos2θdθ=-2sin2θ and    dydθ=d3-sin2θdθ=-2cos2θ Now…

Q: y = 3Arcsin (2x³) -- Arccos(2x³)

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Q: Which of the following represents the volume of the solid generated by revolving the region bounded…

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Q: Determine the integral: x²cosxdx (Α x²sinx-2xcosx-2sinx + C x²sinx + 2xcosx+2sinx + C x²sinx-2xcosx…

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Q: y = Arctan ( 2+x 1-2x

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Q: The length of a rectangle is given by 4t - 3 and its height is √2t, where t is time in seconds and…

A: The area of a rectangle with length L and height H is given by A=L×H. We use chain rule , power rule…

Q: 4 The reverse order of So Say 0 J4y +2 ex² dxdy is equal to e-1 se O None of them O

A: To evaluate the given integral by reversing  the order of the integration.∫01∫4y4ex2 dx dy

Q: Q/IF 3 = sin(x) 0²³²141 y= (4) y = 3/2 I sin(x) cos(x) Prove that

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Q: Which of the following indefinite integral has a general antiderivative of: * 5 1 x4 −²x³ + x² − 7x…

A: We know that integration and differentiation are inverse operations.

Q: lim x²e-x x →∞

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Q: Q3/ Find a volume for the region bounded by 4/X and Y = (X-3)² about the x-axis.

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Q: The given function v = ln (xy) + ex+y Determine Ov/ox

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Q: 3. The auxiliary equation of the differential equation (D² - 6D+9)y = 0 falls under Prove your…

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Q: The general solution of the equation (D4 +D²)y= -12 is A y=c₁ + c₂x + c3cosx + casinx+3x² B y=c₁ +…

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Q: Evaluate the double integral [[ cos(x + y) dA, where R is the region bounded by the lines y = r and…

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Q: 6. Find the area enclosed by the curve x² + 8y + 16 = 0 the x-axis, the y- axis and the x-4 = 0…

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Q: Let f(x)=√√3x-2 on the interval volume of the resulting solid. 83 (A) -unit3 125 83л (B) -unit³ 135…

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Q: 1. f (x² + 1)(x² + 3x) dx

A: To evaluate the given integral.∫x2+1x3+3x4dx

Q: Q1/ Find the area of the region bounded by the given curve (y=x²-5) and the curve (x = = -) by means…

A: Given y=x^2-5 & x=-y/4

Q: Determine the area bounded by the functions f(x) = (x + 1)³ and 1 A -unit² 3 B -unit² 3 -unit² 4 1…

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Q: Evaluate the improper integral A) diverges 3 B 4 с N|9 2 3 -dx

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Q: 1. f In(x+2) dx 2x+4 2. fx² ex dx 3. f tan³x dx 12

A: We know that integration of xn is xn+1 /n+1. And integration of 1/x is lnx +c.   Here i attached the…

Q: e integral be 'solvable' using trigonometric substitution. What is the correct choice of u given J…

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Q: 2. lim x sin(1/x) X18 ex+2x 3. lim X18 ex

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Q: cot3x Lim X-o cotx 0

A: Given limx→0cot3xcotxTo evaluate the limit:

Q: The Minimum point of y = 3x+6

A: Find out the minimum point of the function.

Q: Given the integral sec6 (x - 1) tan4 (x - 1)dx, which of the following equatio useful for…

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Q: 0.06x, solve f'(x) = 130. (Round answer to nearest tenth.) Given f(x) = 250 e X =

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Q: Find L-1 ((₁+1)² (s+1)(s²-1)/

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Q: --——-^*[e'-In(2t+1)]dt, find g'(x) . dx 4 A e*+ (2x + 1)² 4 B et + (2x + 1)² 2 (C) e*- - (2x + 1)²…

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Q: A population of bacteria B has a growth rate proportional to B itself. If between 12:00 nn and 2:00…

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Q: Determine the area bounded by the functions f(x) = (x + 1)³ and g(x)= x + 1 3 A 2-unit² 1 Ⓡ / unit²…

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Q: Stretching spring: Eighteen pounds of force is required to stretch a spring 3 ft. from its natural…

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Q: If y = arcsin (e5e), Check Answer dy da

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Q: The Critical Point of y = xe*

A: Given; y=xe^x

Q: dy Reduce the linear DE (2xy + x²+x¹) dx = (1+x²) dy=0 to standard form dx (A) +y dy dx -2x 1+x² =x²…

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Q: Given; √ √ tex dx 2 Applying rationalizing substitution, find dx in terms (A) z dz 2+z² 2 z dz B…

A: Given query is to find the dx in terms of dz.