Question 13 Evaluate S A B 3x5 3x4+6x³ 3x² - 6x x² - 2x 2 - 4x 2 x² - 4x 2 -dx. using method of partial fractions. 2²- ] + C +C 1/2 ] + C (x-1) 1/6(x+2) 16/3 + In (x+1) 1/2 (x-1) 1/6(x+2) 16/3- (x+1) 1/2 (x-1) 1/6(x+2) 16/3 x+1 + In

Q: S₁ + Sa cos²0 de 01/2000 sin ²0 de csc ³0 de + Sc 01/se sec ³0 de The integral dx (x²+4)² can be…

A: We have to solve above integral

Q: d the equation of the tangent line to the graph at the specified value of x. y=x√3-x², z = 1.

A: Given query is to find the equation of the tangent.

Q: 17. Evaluate the integral or show that it is divergent [(a)-(c)]. 4 6 14 dx (a) wzda, f (b) (b)dx,…

A: As per the instruction, we will be answering the first three subparts. For (a),…

Q: (C) Find dx (i) y= for the following functions : 3x 2x-1 2x+1 (ii) y=sec(sec ¹5x)+e5lmx +4

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Q: ow that lim (x,y) → (0,0) 4 3x² + y² 5y does not exist.

A: To show that limit does not exist.

Q: Evaluate S tan" (x) sec¹x dx. I A tan (+1)(x)tan (-1)(x) + C m+l - 1 I B tan (+3)(x) +tan (+1)(x) +…

A: Let's evaluate given integral.

Q: Evaluate √√√x² + y² ds along the curve r(t)=(4 cost)i + (4sint) j+3tk, -27 ≤t≤ 2T. C

A:

Q: Which of the following refers to backward - difference formula? Why? You can give your own example…

A: We need to compare with general formula of backward difference.

Q: π 5π Find the area bounded by the trigonometric curves y=sinx and y=cosx from x= —to x = 4 1.414…

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Q: 1 3 Find the area bounded by the curve y== -x3. -x² + 3x and the line y=x. 16 10 square units 8…

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Q: Exercises To Solve [No.5] 3dx 9x²6x+5

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Q: Evaluate A B Stan" (x) m+1 D "(x) sec4x dx. tan (+1)(x) +tan (-1)(x) + C m-1 tan (+1)(x)-tan (-1)(x)…

A: topic- indefinite integral

Q: Question 18 The volume of the solid generated by revolving the region bounded by x2=4y and y2=4x…

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

Q: Does y = (x-5)^(2/3) have a point of inflection?  Discuss.

A: The function y=x-523

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: Question 2. Find the limit, if it exists, or show that the limit does not exist. (a) 4xy (2,3)—(0,0)…

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Q: Evaluate tan" (x) sec¹x dx m+ 1 m+1 1 m+2 B D -tan (m + 1)(x)-tan (-1)(x) + C m - 1 (m+1)(x) +tan…

A:

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

A: Solution is here

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

A: Take the integral of the first curve minus the second curve.

Q: Tercises To Solve [No.5]

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Q: x ¹/2 dx and using the substitution y=x1/2, the resulting integral takes the form: x-x 4u -du…

A: We have given integral  I = ∫x12x-x3 dx u=x12 du=12x12-1 dx du=12x-12 dx du=12x12 dx 2du=dxx12…

Q: Skew lines are lines that are not parallel, yet do not intersect such as in this diagram: # Show…

A: We need to show that the 2 given lines are skew

Q: Suppose m and n are constants and m #n. Evaluate [sin (mx) cos (nx) dx.

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Q: өpapzp4=6,ff f f +

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Q: Evaluate Stan" (x) sec¹x dx. 1 -tan (+2)(x) +-tan" (x) + C m+2 m 1 1 -tan (+1)(x) + -tan (™-1)(x) +…

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Q: Consider ·S= x-m+- Sx 3x5 -dx. Using the method of partial fractions, the given integral can be…

A:

Q: What is the value of f(1)- 168 in fx³ Inx dx = f(x) ((1/4) Inx-B) + C? A) 3 B 0 1 2

A:

Q: What is the value of f(1) - 168 in [x³ Inx dx = f(x) ((1/4) Inx-B) + C? 0 1 3 2

A: Let's evaluate given integration.

Q: if a 3 letter word is formed by randomly choosing 3 letters from the word PAINTED, what is the…

A: This question can be solved using the concepts of permutation and combination.

Q: Suppose a population of fruit flies changes at a rate of g(t) = -4e0.041, in flies per day. If the…

A: Topic:- application of integration

Q: Evaluate Stan" (x) sec¹x dx 1 A m+1 I m+3 B 1 -tan (m + 1)(x) +- m-1 1 -tan (m + 3)(x) + m+1 -tan…

A:

Q: QUESTION 3 Evaluate sin(Inx sin (Inx) dx Integration by parts will be used repeatedly. What is the…

A:

Q: 1. Find the surface area of the solid obtained by revolving the curve y = √25-x from = 9 to x = 16…

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Q: Question 12 What is the value of f(1) - 16B in [x³ Inx dx = f(x) ((1/4) Inx-B) + C? (A) 1 B) 3 2 D

A: Please see the below picture for detailed solution.

Q: Question 14 π 5ñ Find the area bounded by the trigonometric curves y = sinx and y=cosx from x = —to…

A:

Q: Use the graph to find the following limits. a. lim f(x) b. lim f(x) x→1 x+3 a. Find lim f(x) or…

A: Here is the solution of the given problem. To, solve this problem we use the simple criteria of…

Q: QUESTION 4 What is the value of f(1) - 168 in x³ Inx dx = f(x) ((1/4) Inx-B) + C? 3 2 00

A: Given

Q: The integral ¹S. 01-fese csc ³0 de sin² sin ²0 de = [sec³ sec ³0 de + cos² cos²0 de dx (x²+4)² can…

A: We have to solve Integral

Q: f(x) = 2x³9x² + 12x − 3 -

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: Solution is here

Q: Question 3 To evaluate (B fr²cost sx dx use integration by parts. What is the expression after the…

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Q: The integral S³ S S Sse x dx x²+√√x²-1-1 sece tane de sece - 1 cose d 1 - sino sine de 1 + cose…

A:

Q: 36. Let d; denote the hours of daylight and 8; denote the increase in the hours of daylight from day…

A:

Q: can be transformed to which of the following when trigonometric substitution is used? (x²+4)² sin ²0…

A: Please see the answer below.

Q: Suppose m and n are constants and 1 1 —sin(m− n)x+ - -sin(m+n)x+C 2 m-n m+n 1 = cos(m− n)x - 1…

A:

Q: Consider two athletes running at variable speeds v₁ (t) and v₂ (t). The runners start and finish a…

A:

Q: Suppose that Find f'(x). f'(x)= f(x+h)-f(x) = -5hx² +6hx + 2h²x + 3h² - 1h³.

A: We will solve the problem.

Q: Question 7 Consider S= Sx- x-m+ A) 5 3x5 3x4+6r³-3x²-6x A B C -+ -+- x-1 x+1 x+m 17/6 14/3 -dx.…

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Q: Find S y dy y+2 using the substitution V +5=√y+2

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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)?…

A: Topic = Integration