What is the dy/dx of y = 3sin²x cos x ? O 3 sin x(sin²x - 2cos²x) O-3 sin x(sin²x - 2cos²x) O 3 sin x (sin²x + 2 cos x) -3 sin x (sin² x + 2 cos x)

Q: Л 5л nd the area bounded by the trigonometric curves y=sinx and y=cosx from x=- to x=-. 4 4

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Q: What is the value of f(1) - 16B in J x³ Inx dx = f(x) ((1/4) Inx-B) + C? (A) 1 B) 0 C 2 D) 3

A: Let's evaluate and then find value.

Q: y dy y+2 (√√y+2=5)(-5√√y+2+y+21) + C 3 B (√√y+2-5) (5√√y+2=y+24) + C 3 © ²² (√√y+2-5) (5√/y+2+y+24)…

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Q: (-2-x)²+5 if x ‡ - 3 = 4x + 17 if x = -3 the following limits. Enter "DNE" if the limit does not…

A: The given function is: f(x)=(-2-x)2+5 if x≠-34x+17 if x=-3

Q: QUESTION 14 Calculate the area of the smaller region (to the left of the parabola) bounded by (x+5)…

A: We need to find area.

Q: A spherical tank of diameter 4 m is half-full of water (weight density = 9800 N/m³). Setup the…

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Q: What is the definite integral on the interval [1,3] given by n lim n-∞ €k cos πæk Δα? 3 of x cos x…

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Q: Evaluate A B с D S= 3x-5 3x4 + 6x3-3x2 - 6x x² - 4x 2 x² - 2x 2 x² - 4x 2 x2-2x-In (x-1) 1/6(x+2)…

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Q: ·S. The integral of sect S S x dx x²+√√√x². sece tane de sece - 1 sec²0 do 1+tano cose de 1-sine…

A: Given Problem:-

Q: The integral O 01 °: June 8 ° sec³ 4 can be transformed to which of the following when trigonometric…

A: Answer is (A)

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

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

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Q: A trough is full of liquid of weight density 9,000 N/m³. The ends of the trough are equilateral…

A: Given:         Density of Liquid ρ=9000 N/m3          Sides of triangle a=2 m     The expression for…

Q: Sta tan" (x) sec4x dx _¹___tan (m + 1)(x) — —__¹___tan (™− 1)(x) + C m+ 1 m-1 ¹__tan (m + 2)(x) +…

A: To find the value of given indefinite integral.

Q: Evaluate tan" (x) sec²x dx m 1 1 n (m + 2)(x) + tan -tan" (x) + C m+2 m 1 -tan (m + 1)(x) — . m+1…

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Q: Calculate the area of the smaller region (to the left of the parabola) bounded by (x+5)^2=2y, the…

A: Solution of the problem as follows

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: What will be the rate of change of the area of a circle with respect to its radius when the radius…

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Q: The integral O cose de 1-sine sec²0 de 1+ tan sece tane de sece - 1 S sine de 1+ cose x dx can be…

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Q: Evaluate sin (Inx n(Inx) dx xsin (Inx) + xcos (Inx) - [sin (In x) dx+C _xsin (Inx) – xcos (lnx) –…

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Q: A manufacturer drills a hole through the center of a metal sphere of radius 5 inches. The hole has a…

A: I am attaching image so that you understand each and every step.

Q: fx²cc use integration by parts. What is the expression after the second integration by parts? x2sinx…

A: Solved below.

Q: Find the value of k that will make the function f 2 if x<-4 . f(x)= -x+3k, if x2-4 Blank 1 Blank 1…

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Q: (d) ƒ COS √1+sin x dx, (e) cos(lnx) S dx Т

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Q: Question 6 Suppose m and n are constants and 1 m-n 01 I 2 N DI 1 sin(mx) cos(nx) dx I -sin(m-n)x+…

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Q: Evaluate the following. 3 1. f(1-√x) dx √X

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Q: Use the table to the right to find the given derivative. d xxx) 1x=5 (Simplify your answer.) |x=5 X…

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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: QUESTION 2 What is the value of f(1) - 16B in | x3 Inx dx = f(x) ((1/4) Inx - B) + C? 3 0 1 2

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Q: A spherical tank of diameter 4 m is half-full of water (weight density = 9800 N/m³). Setup the…

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Q: Find the area bounded by the curve 16 square units 10 square units 4 square units 8 square units 16…

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Q: x-m+ 3x4+6x3 3x2 - 6x A B C — + x-1 x + 1 x+m +. dx. Find the sum of A, B, and C. D

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Q: 13. - (In t ² )º t dt

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Q: = fx²coss x²cosx dx- use integration by parts. What is the expression after the second integration…

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Q: dx The integral can be transformed to which of the following when trigonometric substitution is…

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

A:

Q: Question 12 Consider ·S S(x-1 x-m+ (A) 17/6 B) 14/3 6 D) 5 3x5 3x4+6x²-3x² - 6x A B C + -+ x-1 x+1…

A: Consider ∫3x53x4+6x3-3x2-6x dx. Using the method of partial fractions, the given integral can be…

Q: Calculate the area of the smaller region (to the left of the parabola) bounded by , the x-axis, and…

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Q: 3x5 ·S= 3x4+6x³-3x² - 6x x²-2x-In -1 [ + €². (x-1) 1/6(x+2) 16/3 (x+1) 1/2 +C x² - 4x (x − 1)…

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Q: y dy Find S y+2 O ²(√y+2−5) (5√/y+2−y+24) + C (√y+2−5) (5√/y+2+y+24) + C (√y+2-5) (5√/y+2+y+21) +C 3…

A: A detailed solution is given below.

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

A: ∫xx2+x2-1-1dx=∫secθ.secθtanθsec2θ+sec2-1-1dθ=∫sec2θtanθsec2θ-1+sec2-1dθ=∫sec2θtanθtan2θ+tanθdθ=∫sec2…

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

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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: We have to find the radius of inner circle

Q: The integral dx (x²+4)² sec ³0 de sin ²0 de ° csc ³0 de ° Scos²0 do can be transformed to which of…

A: Here we have to transformed the given integral.

Q: An inverted pyramid is being filled with water at a constant rate of 50 cubic centimeters per…

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

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Q: For the function f(x) = x6 – 10x4 , find the points of inflection.

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

Q: Evaluate S= 3x5 3x4+6x33x2 - 6x + In O x-2 2 x² - 4x 2 O x² - 4x + In 2 x²-2x-In + In -dx using…

A: Given problem:-