Which of the following is or is not an improper integral? Clearly explain your choice. A. ₂ dx B. Jdx C. 2 dx D. dx

Q: [³ sin√xcos√x √x 0 A) None Зл B 256 Зл C 512 3 D 256 3 E 512 - dx is equal to

A: Given, ∫0π24sinxcosxxdx

Q: 3x5 Evaluate 3x4+6x3-3x2 - 6x ^ x² = 4x + 1 [ (x-1) 1/6 (x + 2) 16/3] + A In +C 2 1/2 16/3 B -2x-In…

A: Given that       ∫3x53x4+6x3-3x2-6xdx  We can re-structure this integral as…

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: QUESTION 13 Is this statement true or false? An infinite sequence (a) is convergent only if lim a, =…

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Q: √ ² si 2 63 16 105 2n C 63 D) None Evaluate: A (B 2 sinxcos³xdx is equal to

A: Given query is to find the integral.

Q: 25

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Q: Evaluate tan" (x) sec¹x dx² A −tan (m+2)(x) + — tan” (x) + C m+2 1 −tan (m+3)(x) +_¹__tan (m+1)(x) +…

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Q: dx 2. The integral S can be transformed to which of the following when trigonometric (x²+4)²…

A: Please see the answer below

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- 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: Find the area of the region lying between the inner and outer loops of the limacon r = 1-2 sin θ

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

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

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Q: Previous question Using the definition of the derivative, find f'(x). Then find f'(1), f'(2), and…

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Q: 10. 2 x² +8 X + 2 אן dx

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Q: -x² 9 d. f (x) = xe [0, 5]. e. f(x) = |x² − 4], [0,3]. sin x f. f(x) = = [-ㅠ -π, π]. x² + 1

A: As per our guidelines we can answer only 1 question so kindly repost the remaining questions…

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 f(7) (-2) of f(x) = - +2x - 7x³ + ³² + 5x +1? 3x² 2

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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: 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…

A: Given: y=3sin2⁡xcos⁡x To find: dydx We know that ddxcosx = -sinx ; ddxsinx = cosx

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: 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: 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: 11. 5 [ese xdx

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Q: Exercises To Solve [No.5] 3dx 9x²-6X+5 1

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Q: 18. f(tan 2x + cot 2x)² dx

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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: 7. [(In x)² dx

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Q: (cos-¹2w) 6. ¡ COS dw √1-4w²

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Q: 20. For A. B. C. D. S x1/2 dx and using the substitution u=x1/2, the resulting integral takes the…

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

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Q: Inx Complete the following table to evaluate the limit lim X-400 √x Step Explain the step In x lim…

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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: 17. fe-Inx √√In x² dx 3

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Q: y=(-4x²-5x²) (7x - 2)

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

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Q: A particle is moving with acceleration a(t) = 30t + 8. its position at time t = 0 is s(0) velocity…

A: topic- integration

Q: C) 8 square units

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Q: Find the area of the region bounded by y = x^2 + 2x -6 and y = 3x. Determine the area of region…

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Q: Find the area of the region lying between the inner and outer loops of the limacon r = 1 – 2 sin θ

A: Solution of the problem as follows

Q: S- Find y dy Vy+2 using the substitution u +5=√√x+2. A ²/ (√x+2-5) (-5√/y+2+y+21)+C ℗ ²/(√√y+2-5)…

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Q: Lemma*: If z(x, y) = W+H, then xZx + y2y = (xWx+yWy) + (xHx + yHy).

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Q: What is dy/dx of the given function ³ - 2y² = 6 ? 0-²2 3:² CHE o 3,212

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Q: 3x5 S 3x4+6x³-3x2-6x x²-2x = 2 [ (x-1) 1/6 (x+2) 16/3 (x+1) 1/2 ® [ B x² - 4x 2 x-1) 1/6(x+2) 16/…

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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: 7. 1-3√√x X 2 X √ √ 3 -dx

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Q: 2. Find the horizontal asymptotes of the following functions. √9r²+1+2x+1 (a) f(x). 4x +3

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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: S= Evaluate Ox² - 4x 2 Ox²–2x 2 O x² - 2x - In x² - 4x 2 3x5 3x4+6x + In 3x² - 6x - (x-1) 1/6(x+2)…

A: Explained below