The figure to the right shows four regions bounded by the graph of y=xsin x: R₁, R₂, R3, and R4, whose areas are 1, à-1, +1, and 2-1, respectively. Use this information to evaluate the following integral. 2x S 0 x sin x dx +++++ Area = 1 R₂ y = x sin x R.1 15 Area = -1 77 Area = +1 R₁ R₁ 2T x Area = 2-1

Q: 7√2 2 0 x² 49-x² dxl

A: The given integral,        ∫0722x249-x2dx

Q: defined on the interval [-5, 7]. a.) f(x) is concave down on the open b.) f(x) is concave up on the…

A: This question can be solved using the concept of point of inflection, critical point and point of…

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Q: Test the series below for convergence using the Ratio Test. Σ n=1 n! The limit of the ratio test…

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Q: Q2: Solve the following in 7x²+14x+15 (1) f dx ; (x²+3)(x+7)

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: FIND: hf(x)dx 2 g(x) dx = = f₁₁ f(x) dx = = if g(x) is an odd function. if f(x) is an odd function.

A: We need to find integral.

Q: Solve the initial value problem 25y" — 40y' + 16y = 0, y(0) = 2, y'(0) = 3. y(t): How does the…

A: We can solve this as follows:

Q: (A): Solve the following linear equations by Cramer's rule: x + y + 2z=1 2x-y-z = 0 = 4 x +2y-z

A:

Q: Q5: Find for the following functions: dx (1) In(x - y) = xy + y³ ; (4) y = x sinh 2x -cosh 2x (2) y…

A: We need to find derivative. As per Bartleby's guidelines we can solve one question from multiple…

Q: Q4: (chose one only) 3-x 1- f(x) = 2 x 2 a) Find limx→2+ f(x), limx→2- f(x) andf(2). b) Dose limx-2…

A: Since you have posted multiple questions i can do first question as per our company guidelines…

Q: J 24 tan3 xdx

A: topic- indefinite integral

Q: Q5: Find d for the following functions: dx (1) In(x - y) = xy + y³ ; (2) y = tan³ √cot(7x) ;

A: We can solve the answers as below by finding the derivatives.

Q: Solve the given initial-value problem. y" + 6y'7y= 11e²x, y(0) = 1, y'(0) = 1

A: Given :y''+6y'-7y=11e2x

Q: (A): solve the following linear equations by Cramer's rule: x + y + 2z = 1 2x-y-z = 0 x +2y-z = 4

A:

Q: 38.Calculate the surface area of the surface obtained by revolving the curve y = √9-x² around the…

A: Note to student :    Thanks for posting your queries. But there are multiple questions given. As per…

Q: use triple scalar product to find the volume of the parallelpiped u= v= w=

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Q: Find the general solution of the following differential equation. 64y" +80y + 25y = 0 NOTE: Use c₁…

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Q: Q3 :(A): By using "L' Hopital rules "; Find the limits of : (1) limx-ol: 1-cos x - sin²x

A:

Q: Find the sum of the series. 5(-1)^²n +1 Σ 62n + 1(2n + 1)! n = 0 62n +

A: The sum is evaluated below.

Q: Use the figure below to find the exact value of the trigonometric function of angle A. csc (A) 7 5 A

A: We have to find the exact value of the trignometric angle A, csc(A)=? Since ABC is right triangle,…

Q: |-*^= 39. What is the length of the curve y = √x- between x = 0 and x = 2?

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Q: The area of an ellipse with axes of length 2a and 2b is given by A = Tab. Approximate the percent…

A: Concept: We have given the Area A=πab Here the length a is increasing by 2% which is daa=2% Here the…

Q: A rectangular pen will be built along the side of a large barn. Three sides will be made of fencing,…

A: A rectangular pen will be built along the side of a large barn. Three sides will be made of fencing,…

Q: (B): Find the unit vector perpendicular to the vectors: 3i - 4j + 5k 4i + 5j - 6k du

A:

Q: Let f(x) = 6x√√x + f'(x) = -∞0 8

A:

Q: -1 t² Vta 6 dt

A:

Q: Q2: Solve the following integrals: (3) √ √dx dx (4) fxe* dx

A:

Q: (B): If A = 2i +3j - 4k; B = 3i - 4j+5k and C = i + j-k, find: (iv) (3A + 4B).C (i)A.B (ii) B.C…

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Q: Q5: Find dx (1) In(x - y) = xy + y² : (4) y = x sinh 2x-cosh 2x for the following functions: (2) y =…

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Q: Evaluate the integral and check your answer by differentiating. x8+8x5 - 1 x7 S dx = +C

A: To find out the integration.

Q: Use the figure below to find the exact value of the trigonometric function of angle A. cos(A) 0.49 X…

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Q: Use the figure below to find the exact value of the trigonometric function of angle A. sin (A) 6 A…

A: it is very basic question of trigonometry.

Q: prove that :: 2) (1+i) (1-1)² = 64

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Q: 3 2.)f x³ (4 + x²)² dx ; Use rationalizing substitution

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Q: Q2: Solve the following int (1) dx 1 (x+3)(x+7)

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Solve the given initial-value problem. y(x) = y" + 6y' - 7y = 11e2x, y(0) = 1, y'(0) = 1 -7.x 2x 7e…

A:

Q: Differentiate implicitly to find dy/dx. cos(x) + tan(xy) + 4 = 3

A: Given: cosx+tanxy+4=3We need to find dydx.Recall the formulas: ddxcosx=-sinx…

Q: Find the general solution of the following differential equation. y" - 4y + 7y=0 NOTE: Use c₁ and c₂…

A: Given y''-4y'+7y=0

Q: Q2: Solve the following integrals: (1) 7x²+14x+15 (x²+3)(x+7) dx ; (2) sin6 x+cos6 x sin ³ x cos³ x…

A: According to our guidelines, we can answer only one question or three subparts of a question.other…

Q: Use the figure below to find the exact value of the trigonometric run tan(A) 7 A

A: The solution is given below

Q: Q1: Fill in the blanks for the following statements (chose five only) 4n 1. lim-00 2n+1 2. log10 (3x…

A:

Q: Find the tangential and normal components of the acceleration vector. r(t) = cos(t)i + sin(t)j + tk…

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Q: Q3 (A): By using "L' Hopital rales "; Find the limits of: (1) limal; (2) Itm X(tan-¹x-x)

A: I have solved step by step in detail...go through the solution

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A: Given:

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Q: Find the general solution of the differential equation y" − 6y' + 58y = 0. NOTE: Use c₁ and c₂ as…

A: This given differential equation is 2nd order homogeneous linear differential equation .

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Q: S 2 (2x² + 1) dx

A:

Q: Solve the given initial-value problem. y(x) = 7e y" + 6y' - 7y= 11e2x, y(0) = 1, y'(0) = 1 2x -7.x +…

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Q: Q5: Find for the following functions: dy dx (4) y = x sinh 2x - cosh 2x

A: