+∞o Evaluate: S e-x dx 0 A + ∞ (divergent) B 0 C 1 D) None E e

Q: QUESTION 9 Calculate the area of the smaller region (to the left of the parabola) bounded by (x+5)…

A: Please see the below picture for detailed solution.

Q: fax² ax² + bx dx is equal to O ax³ bx² ㅇㅇ + C 3 2 ax³ bx² 3 2 a²x³ 6²x² 3 2 a²x² 6²² 3 2 O + + + +…

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Q: Symmetric equations of a line with direction vector d = (5, 3, -4) and z-intercept of 7.

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Q: S₁ A B If 2x²+x-2 (x+1)(x²+1) ² 1 -- 2 U NIG 5 —— D E) None + -S₂ -dx = A x + 1 + B (2x) + C x²+1…

A: Partial fraction decomposition

Q: Question 11 Evaluate: S₁ 2 A 63 16 B 105 C) None 16″ D 105 E 2π - 63 sinxcos³xdx is equal to

A: In given problem we solve definite integral using substitution method .

Q: Consider ·S= √(x-m+ A₁ 17/6 14/3 3x5 3x4+6x33x² - 6x с B -+ x+1 x + m -dx Using the method of…

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Q: 5. 4 f sin + 2zdz

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Q: 10. 3 J√cos z sin ³ zdz COS

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Q: C) 8 square units

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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: B D E 2x None 2 A √ N dx is equal to

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Q: QUESTION 1 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: 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…

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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: Find S- y dy using the substitution u +5=√y+2. y+2 (A) (√3+2-5) (5√/F+2-1+24) +C 3 B…

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Q: A -2 f Coxx dx x’sinx + 2x cosx – 2 dx + C

A: Using integration by parts,we got correct answer as option -(A)

Q: Find the area bounded by the curve 4 square units 10 square units 8 square units 16 square units 3 y…

A: Area

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: Suppose m and n are constants and m # n Evaluate O 1 1 -cos(m-n)x - - -cos(m+n)x] + C m-n m+n O 1 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: Please see the below picture for detailed solution.

Q: 11. fel/x²di .3 X хр

A: Here, to evaluate: I=∫e1x2x3dx

Q: 2. Given u = 8i - j + 3k and v = 7j - 4k, compute each of the following. (a) -3v (b) 12u + v (c) ||…

A: In this question, we have given two vectors u and v. We want to compute the given expression.

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

A: topic - integration by parts

Q: 17. fe-Inx √√In x² dx 3

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Q: St dx tan 1²dt=2x tan x² X (A) True B) False

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Q: x² - 16 to fill in the table: - 4 5 4.5 4.1 4.01 Based on ONLY the table of values above, what…

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Q: 9. 5 3 2 S 2 3 S ds

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Q: ·S- Find y dy Vy+2 using the substitutionu +5=√√y+2. A √y + 2 − 5 ) ( 5 √√y + 2 + y +24) + C (В…

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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: 2. [e1/² cos 2tdt Set/2

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Q: Evaluate A B D Stan" tan" (x) sec4x dx. —tan (™+3)(x) + _____tan (™ + 1)(x) + C m+1 1 −tan (™+2)(x)…

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

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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: Question 14 The integral x dx can be transformed to which of the following using trigonometric…

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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…

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Q: The integral O [se Ss S S sec²0 de 1+ tane sece tane de sece - 1 O x dx x²+√√x²-1-1 sine de 1+ cose…

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Q: Question 21 Consider S x-m+ 17/6 B 5 6 14/3 3x-5 3x4+6x3-3x2 - 6x A B C + + x-1 x+1 x + m -dx. Using…

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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: Evaluate 1 m+3 1 m+ 1 I M+2 T }}}+1 tan" (x) sec¹x dx I -tan (m + 3) (x) + m+1 1 -tan (m + 1)(x) +…

A: SOLUTION-

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

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Q: (e) x = = 2y², x = 4 + y² - (f) x = 1 — y², x = y² – 1 32 Answers (a), (b), (c) In 2-1, (d), (e)…

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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: 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: 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: c) Parametric equations of a line that goes through P(1, 3, 5) and is perpendicular to the line (1,…

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Q: The graph of f(x) passes through the point (4, 0). The slope of the line tangent to the graph at the…

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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: 3. 2 [sin 4 3x cos² 3xdx

A: 3. To evaluate the ∫sin43x cos23x dxFormula: (1) cos2x=1-sin2x(2) ∫sinn xdx=-1n sinn-1x cos x+n-1n…

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