(D³ - 3D²D + 3)y = 0

Q: 4. Being careful to allow for parts of the curve being both above and below the x-axis, determine…

A: Being carefule to allow for parts of the curve being both above and below the x‐axis, to determine…

Q: ‹S- A S Ⓡ /- © /- S- D For dx and using the substitution = x1/2, the resulting integral takes the…

A: Just use the substitution and find the required integral. Option (B) is correct.

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

A:

Q: Consider 12-1 S= x-m+ 3x5 3x4+6x33x2 - 6x A B C + x-1 x + 1 x+m (A) 14/3 (B) 17/6 C) 5 6 —+ -dx.…

A:

Q: 9. [cos° { xsin’ } xdx

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

Q: What is the of y = (tan-¹4x)² ? 2 - 2tan ¹4 1+16x² 1 8tan ¹4x 1+16x² 2tan-1 ¹4x 1+16x² -1 8tan ¹4x…

A:

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

A: We can rewrite the given integral by using this substitution u = x1/2

Q: QUESTION 15 Find the area bounded by the curve y = 16 4 square units 16 square units 10 square units…

A:

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

A:

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

A:

Q: If tan A = and tan B B = 1/1, calculate and simplify the following: tan (A - B) = [?]

A: SOLUTION-

Q: S x dx x²+√√x²-1-1 The integral substitution? (A) [sec²0d0 1+tan cose de (B) 1-sine sece tane de…

A: Simplify and substitute x = sec θ to get the answer.

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…

A:

Q: y dy Find ·S- √y+2 03 (√x+2-5)(-5√/y+2+y+21) + C ○ ² (√y+2−5)(5√/y+2+y+24) +C 3 (√√y+2-5)…

A:

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

A:

Q: Being careful to allow for parts of the curve being both above and below the x-axis, determine the…

A: Solution of given question is written in below steps.

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: I 5л Find the area bounded by the trigonometric curves y=sinx and y=cosx from x=— tox=³ 3.667 square…

A:

Q: 3 Find the area bounded by the curve y=-x3- 16 A) 8 square units (B) 10 square units C 4 square…

A: The region is bounded by the curves y=116x3-34x2+3x and the line y=x

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

A: To solve the given integral problem.

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

A: Given

Q: 7. 1-3√√x X 2 X √ √ 3 -dx

A:

Q: One of the correct steps to evaluate A B) None Ⓒ [+ + [ 1².40-16.4040] -S de cos 40d0 + [ 140 + 1 =…

A:

Q: 4. Being careful to allow for parts of the curve being both above and below the x-axis, determine…

A: We need to find area.

Q: Differentiate the following functions using Chain Rule: 1. y = (4x + 3)²

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: The integral S sine de 1+ cose sec²0 de 1+ tan cose de 1-sine sece tane de sece-1 S x dx x²+√√x²-1-1…

A: dsecθdθ= sec θ.tan θ

Q: 14. Solve the initial-value problem dy dt = -2y + u₂(t)e¯¹, y(0) = 3.

A:

Q: y dy Find ·S- using the substitution +5=√√y+2· Vy+2 ²(√y+2−5)(5√/y+2+y+21)+C 3…

A:

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)…

A:

Q: Find y dy ·S- using the substitution +5= √√y+2 U /y+2 /y+2−5) (5√√y+2+y+24) + C…

A:

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

A:

Q: 1/2 S x²√1-x²dx. 0

A:

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

A:

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: QUESTION 2 Evaluate lim " QUESTION 3 Clearly illustrate with explanations why lim 100 0.01F g(x) x-0…

A: We have to find limit

Q: Supposem and n are constants and m #n. Evaluate sin(mx) cos(nx) dx² 1 A -sin(m-n)x+ -sin(m+n)x +n)x]…

A:

Q: -S- A Ⓡ / T B C S (D) S- For x1/2 dx and using the substitution u=x¹ x1/2, the resulting integral…

A:

Q: 100t Consider the population function p(t) = t+9 a. Find the instantaneous growth rate of the…

A: The given population function is pt=100tt+9.   a. The objective is to find the instantaneous growth…

Q: y= (4x² + 2) (4x3³ - x)

A: Here we have to evaluate y=4x2+24x3-x

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: y = 4 16 3x+3

A:

Q: Find the cross product a x b. a = (7, 6, -5), b = (2, -1, 1) Verify that it is orthogonal to both a…

A:

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

A:

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

A:

Q: Evaluate sin (Inx) dx. Int second integration by parts

A:

Q: 18. S sin xdx 2-cos² X

A: The given integral is: I=∫sinx2-cos2xdx    ...1 As we know the common integral; ∫11-x2dx=sin-1x+C

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

A:

Q: dx 3-2x-x²

A: We need to solve : ∫-10dx3-2x-x2

Q: Given: 3z = xy Find fy O xy/3 Oy/3 Ox/3 O None of the choices

A: We can find the partial derivative as below

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

A: