Equation xdy + ydx = 0 y"-3y" + 3y + y = 0 (y)¹/² = √/(1+y")4 Order Degree Kind IV DV

Q: Suppose m and n are constants and m + n. Evaluate [sin (mx) cos(nx) dx- A) Ⓒ[-(-)-(+)₁]+€ m+ncos (m…

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Q: A balloon is released from the ground 100 meters from an observer. The balloon rises directly upward…

A: We have to choose to correct option

Q: Let f(x) = 8x³ - 4. What is the value of c on the interval [0,2], such that f(c) equals the average…

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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: We need to setup integral.

Q: Find the area bounded by the curve y=x³x²+3x and the line y=x. 16 (A) 8 square units (B) 4 square…

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Q: QUESTION 7 Evaluate 3x5 3x4+6x³-3x² - 6x x²-2x-In O x²-4x 2 O x²-4x 2 O rẻ-2r 2 [(x-1) 1/6(x+2) 16/3…

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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…

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Q: Moving to another question will save this response. 3x5 ·S. 3x4+6r3-3x2 - 6x 0 5 06 O 17/6 A Moving…

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Q: ·S- For x1/2 S- S. dx and using the substitution -du U 1-u² 4u -du 4u 4- (21²) ² U -du 1-u4 -du u=x…

A: We have to solve Integral

Q: X-1 (x - 2)² 5. S dx

A: We have to evaluate the integral.

Q: 5 S dx (x-3) ² (A) None B 0 C ∞o (does not exist) D - 1 E 1 Evaluate:

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Q: Find the area bounded by the curve y=-x³ 1 - 16 A 8 square units B 16 square units 10 square units 4…

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Q: Question 18 Find - y dy (y + 2 A(√y+2-5) (5√/y+2+y+24)+C А Ⓡ(√y+2-5)(-5√/y+2+y+21)+C B Ⓒ(√3+2-5)…

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Q: Using chain rule, what is the (2x-¹-3x)³ ? da O 24+108x²+54xª+81x6 x4 -24+36x²+54x4 -81x6 x4 O…

A: The objective of the question is find the derivative .

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

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Q: To evaluate x²cosx dx' use integration by parts. What is the expression after the second integration…

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Q: What is the derivative of h (x) = (7x³+4x)" ? Oh' (x) = 7(7x³+4x)6 ○ h' (x) = 7(7x³ + 4x)º (21x² +…

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Q: 7. [(In x)² dx

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Q: Question 2 S y dy Find √x+2 A ² (√x+2-5) (5√/y+2+y+24) + C 3 ℗ ²² (√5+2-5) (5√/y+2+y+21) + C B…

A: GIVEN

Q: 5ñ Find the area bounded by the trigonometric curves y=sinx and y=cosx from x=to x== 4 (A) 3.667…

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Q: Suppose m and n are constants and m #n. Evaluate sin(mx) cos(nx) dx A − cos(m− n)x+ · -cos(m+n)x] +…

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

Q: 6) INVERSELY LOGARITHMIC The following information is given about a logarithmic function of the form…

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Q: Question Given compute the following integral. Provide your answer below: (-4f(x) + 4g(x)) dx = […

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Q: 9. [cos° { xsin’ } xdx

A: The objective of the question is evaluate the indefinite integral.

Q: -6 -4 -2 0 --2 (-2,-3) 2 6 4 (-1,-4) 1. Does this graph have a horizontal shift? If yes, state the…

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Q: 1 Find the area bounded by the curve y=- =-=-—-—-x³-3³² x ² + 16 4 -x2 + 3x and the line y=x.

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

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Q: Find the area bounded by the curve y = 16 A 16 square units (B) 8 square units 10 square units 4…

A: Find the area bounded by the curve y= 1/16x3-3/4x2+3x and the line y= x .

Q: What is the derivative of the following? sin(t) d dt f 117 da cos(t) s(t) 4-sin² (t) 1 4 — sin² (t)…

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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: 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: Find y dy ·S= using the substitution u +5=√√y+21 Vy+2 ²/(√√y+2-5) (5√√y+2+y+24) +C…

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Q: QUESTION 19 A trough is full of liquid of weight density 9,000 N/m3. The ends of the trough are…

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Q: ·S= Evaluate 3x5 3x4+6x³-3x² - 6x + In x² - 4x 2 x² - 4x 2 x²-2x-In x² - 2x 2 -dx using method of…

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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…

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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: Please see the below picture for detailed solution.

Q: QUESTION 8 The integral O S fec S S O O ·S- O x dx x²+√√√x²-1-1 sine de 1+ cose sec²0 de 1+tane cose…

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Q: 2y”” − 3y" — 3y² + 2y= (e* + e*)²

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Q: Use the table to the right to find the given derivative. d[ f(x) dx x + 7 X = 5 = (Simplify your…

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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: If 1500 square centimeters of material is available to make a box with a square base and an open…

A: We can solve the given problem by using the second derivative test.

Q: Evaluate • O Stan" (x tan O m+1 1 m+3 1 m+2 m+1 "(x) sec¹x dx n (m + 1) (x) — __ ¹ (m+3)(x) + n (m +…

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

A: We have to solve integration

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

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Q: What should be the shape of an oval field complying to a given circumference, if it is to have a…

A: Given :The shape of an oval field complying to a given circumference, if it is to have a maximum…

Q: dx can be transformed to which of the following when trigonometric substitution is used? (x²+4)²…

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Q: dx can be transformed to which of the following when trigonometric substitution is used? (x²+4)² A +…

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

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

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Q: St. -4 16-x² A 4 (В 2 (C) 0 (D) None (Ε 8 00 dx is equal to

A: This is based on the definite integral.

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

A: Solution of the problem as follows