QUESTION 1 Consider x sinx cosx dx = f(x) sin2x - g(x) cos2x + C. What is the value of f(1) + g(1)? O 1/2 O 1/4 3/8 1

Q: Find the area bounded by the curve y=-x³ 16 (A) 8 square units B) 4 square units C) 16 square units…

A: Take the integral of the first curve minus the second curve.

Q: π 5π Find the area bounded by the trigonometric curves y=sinx and y=cosx from x= —to x = 4 1.414…

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Q: 5л Find the area bounded by the trigonometric curves y=sinx and y=cosx from x= to 3.459 square units…

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Q: The table below shows the average rates of change for points near In (2) for the function f(x) = e +…

A: We have to find the instantaneous rate of change

Q: Which of the following is an acceptable answer, when we are asked to evaluate f 5+x² O In sec+tan 0…

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Q: 3x5 S= -dx. Using the method of partial fractions, the given integral can be written as…

A: Solution: ∫x53x4+6x3-3x2-6xdx

Q: (5 Lim 9-5 dx S a -x²-8x-15

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Q: The volume of the solid generated by revolving the region bounded by x2=4y and y2=4x about y=4 is to…

A: Solution is here

Q: Consider ! x sinx cosx dx = f(x) sin2x - g(x) cos2x + C. What is the value of f(1) + g(1)?

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Q: Estimate the slope of the tangent line to the curve at the given point (-0.5,4.998) on the graph to…

A: It is clearly seen in the figure that the tangent line is horizontal to the x axis at the point…

Q: y dy Find ·S- using the substitution +5=√√√y+2 √√y+2 (√x+2-5)(-5√/y+2+y+21) + C © ²/(√x+2-5)…

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Q: S ' | Sc Sex²0 The integral dx (x²+4)² see c³0 de s²0 de csc ³0 de sin ²0 de can be transformed to…

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Q: Let S be the solid inside the sphere p _ 6cos@ and below the cone Ø = π/4 Find the volume of the…

A: S be the solid inside the sphere ρ=6cosϕ and below the cone ϕ=π4

Q: [ sin(mx) cos(nx) dx- D Suppose m and n are constants and m #n. Evaluate 1 1 A -cos(m-n)x- =…

A: This question can be solved using the concept of integration of trigonometric functions.

Q: Evaluate tan" (x) secx dx. 1 A n(m + 1)(x). m+1 1 (В -tan (m + 2)(x) + m+2 1 -tan (m+1)(x). m+1 1…

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Q: ·S- sece tane de sece - 1 The integral S S x dx x²+√√√x²-1-1 sino de 1+ cos cose de 1-sino sec²0 de…

A: The objective is to find the correct option.

Q: Suppose that f(x, y) = √√/4² -2² - y² on the domain D = {(x, y) | x² + y² ≤ 4²}. Q Then the double…

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Q: Question i: Kim is needing $3000 for a trip. she can make an investment that offers an interst rate…

A:

Q: Question 3. Let L₁ be the line with parametric equations x = = 1 — t, y = 3 — 2t, z = 4t. Let L₂ be…

A: Given L1: x = 1-t , y = 3-2t , z = 4t Rewrite it in the following form (x-1)/-1 = (y-3)/-2 = z/4…

Q: Evaluate [sin (Inx) dx Integration by parts will be used repeatedly. What is the expression after…

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Q: he definition of the derivative, find f'(x). Then find f'(-3), f'(0), and f'(4) when the derivative…

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Q: To evaluate te use integration by parts. What is the expression after the second integration by…

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Q: Given the following planes: 1. 2x - y - 6z = 5 II. (x-1, y - 1, z - 6) * (3, 1, 1) = 0 III. (0, 8,…

A: Topic: Plane in three dimension geometry The solution is given below:

Q: luate sin (Inx) dx Integration by parts will be used repeatedly. What is the ression after the…

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Q: The volume of the solid generated by revolving the region bounded by and y2=4x about y=4 is to be…

A:

Q: Evaluate sin (Inx) dx Integration by parts will be used repeatedly. What is the expression after the…

A:

Q: Evaluate sin (Inx) dx. Integration by parts will be used repeatedly. What is the expression after…

A: Given:∫sin (ln x) dx Let I=∫sin (ln x) dx By using integration by parts method, ∫udv=uv-∫vdu Let…

Q: QUESTION 12 Evaluate Stan" (x) sec¹x dx 1 -tan (m + 1)(x) + m-1 -tan (m + 1)(x) - — ¹ m-1 -tan (m +…

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Q: Find ¹₁ (5z + 2y)dA where D = {(2, y) | z² + y² ≤ 16, z ≥ 0}

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Q: Consider and C. -dx Using the method of partial fractions, the given integral can be written as…

A: Here, 3x53x4+6x3-3x2-6x=x-m+Ax-1+Bx+1+Cx+mor, x4x3+2x2-x-2=x-m+Ax-1+Bx+1+Cx+mor,…

Q: For O x 1/2 -dx and using the substitution=x1/2, the resulting integral takes the form: -du du -du…

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Q: Question 4 Evaluate sin (Inx) dx- Integration by parts will be used repeatedly. What is the…

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Q: The integral A / B © S D x² + x dx can be transformed to which of the following using trigonometric…

A: Explained below

Q: Evaluate Stan" (x) sec¹x dx. 1 A 1 -tan (m+3)(x) + m+3 m+1 1 tan (+2)(x) +-tan" (x) + C m+2 m 1 tan…

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Q: º fun"(x) sec¹x dx tan Evaluate

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Q: Evaluate (A) B ze Stan" (x) sec²x dx- D tan (+2)(x) +-tan" (x) + C tan (+3)(x) +tan (+1)(x) +C 1 1…

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Q: The volume of the solid generated by revolving the region bounded by x²=4y and y2 = 4x about y=4 is…

A: The full solution of the question is given below:

Q: Exercises To Solve [No.5] dx 05². of зах (2) x²+2x+5 9x²6x+5 D

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Q: Secor, x²cosx dx use integration by parts. What is the expression after the second integration by…

A: We have  to solve above integral

Q: Suppose m and n are constants and m #n. Evaluate I sin O 1 1 -cos(m-n)x- - cos(m+n)x+ C n-m m+n 1 1…

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Q: To evaluate x²cosx dx' x2sinx+2x cosx – 2 x2sinx+2x cosx – 2 x²sinx- – 2x cosx — 2 x2sinx – 2x…

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Q: y dy Find S- y+2 A ²/(√x+2-5)(-5√/y+2+y+21)+C ℗ ²/(√3+2-5) (5√/y+2-y+24) + C B Ⓒ(√x+2-5)…

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: What is the value of f(1) - 168 in [x³ Inx dx = f(x) ((1/4) Inx-B) + C? 0 1 3 2

A: Let's evaluate given integration.

Q: A ²/ (√x+2-5) (5√y+2+y+21) + C 3

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Q: ·S- x² + sece tane de sece - 1 e integral sec²0 de 1+tan cose de 1-sin sine de S x dx can be…

A: We have to find the integral

Q: The volume of the solid generated by revolving the region bounded by x2=4y and y2=4x about y=4 is to…

A: using circular ring method evaluate the volume

Q: Evaluate sin (In (Inx) dx. Integration by parts will be used repeatedly. What is the expression…

A:

Q: For x1/2 dx and using the substitution = x 1/2, the resulting integral takes the form: 4u -du -du…

A: topic- indefinite inegral

Q: The integral S x dx x²+√√x²-1-1 can be transformed to which of the following using trigonometric…

A: Please follow the next step.

Q: (в Suppose m and n are constants and m #n. Evaluate 1 (A) √ [n² m² -cos(m− n)x-- -cos(m+n)x] + C m+n…

A: To solve the given integral.