(d) Sketch the region bounded by the curve y = sin 2x, y = cos x and the line x=0 and x = 2 %3! Hence find the area of the region.

Q: Using Integration By Parts, x sec - x tan x dx = %3D

A: Use integration by parts.

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A: Let's find.

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A: To find the points on the ellipse 5x2+y2=5, that are farthest away from the point 1, 0.

Q: If 7-4/3 = Vx-Vy, determine the values of x and y. %3D

A: We have to find the values of x and y from the above expression.

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Q: Question 3 6x³e**3 dx. using integration by parts Svdu) and letting = UV u= f(x), dv= 3 g(x) dx,…

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Q: dx 4 sin e+C express the answer in terms of x. 3 Using Trigonometric Substitution (x² + x + 1) 2 4/3…

A: Given problem:-

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Q: Find the area bounded by y = x+ 4 and y = x2 - 2. Answer:

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Q: Given the equation below, find dy/dx* 6x^3+2x^30 y+y^4= 9 dy/dx= Now, find the equation of the…

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A: We can solve as follows

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Q: 3r + cos r 2. Use Squeeze Theorem to evaluate_ lim 1-00 V1 +r2 - 5x

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Q: Consider . x2 +2x- 10 2 2 (2x + 4) +1 dx evaluate dx = x² (x² + 4x + 5) (2x+4) +1 dx - x² + 4x +5 -…

A: Topic = Integration

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A:

Q: dx Using Trigonometric Substitution -sin e+C express the answer in terms of x. (x² + x + 1)7 4х+2 +C…

A: Given ∫dx(x2+x+1)32=43 sinθ +C

Q: S****2 x² + x +2 Evaluate x2 – 1 x+ In- (x – 1)2 +C x+1 x+1 x+ In- (x- 1)2 +C x+1 In- +C (х-1)2 о.…

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Q: ху x+

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Q: dx - [f(e)de find f(e) - S. (x² + x + 1) 2 Using Trigonometric Substitution O 3 sec? e 4 4 3 sec? e…

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Q: 4. Given [2r + 5], 4- 2x 1² – 2x' if r < -1 f(x) = if –1<x< 2. sin(r – 2) 2 if r 22 a. Discuss the…

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Q: c. r cos y = " - - log(x³ + y)

A: As per rule of bartleby we can solve only one question at a time and we can solve only three subpart…

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Q: x³ + 6x² + x+2 s ax + In[cx + 1}*(x² – x + 1)°| + fx-1 Tan-1. V3 The resulting integral of x³ +1 +…

A: use simple integration formula.

Q: _14. Suppose that a function f: R² → R and its partial derivatives up to the third orders are…

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Q: 8. dx +x2 Integrate:

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Q: Suppose that f(x) is a differentiable function satisfying the table below. 0 2 f(x) | 1| 2 | 12 | 7…

A: The objective of the question is showing that there exist at least one x=c for which f'(c)=5.

Q: dx + (1 – x²)cot y dy = 0

A: Given problem :- dx + (1-x2 )cot(y) dy = 0 Find the general solution of given differential equation

Q: 2. y-10 4. y=-7x+10 6. y=-2x + 3x

A: Since you have asked multiple question, we will solve the first 3 question for you as per our guide…

Q: Compute f'(a) using f' (a) f(а + h) — f(a) = lim f(x) or f'(a) = lim f(a) for f(x) = 10x³, a = 2.…

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Q: Determine the general equation of the plane 2 passing through the point P (1, -4, -5) and parallel…

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Q: dx consider Using trigonometric substitution, find u ar (x²+x+1)½ (A) u=x+1, a=- (B u=x+1, a=1 C)…

A: Topic:- application of integration

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Q: cos. Given: tan x |dx. Using trigonometric transformation , the integral in terms of u is m ( u ™ )…

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Q: Find the absolute maximum and absolute minimum values of f on the given interval. f(x) = 4 + 54x –…

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Q: x² + x +2 Evaluate x2 – 1 (x– 1)2 - In- - +C x+1 x+1 In- (x- 1)2 +C X+1 x+ In- (x – 1)2 (x – 1)? +C…

A:

Q: cos2x – sin2x cos2x dx = For -F(x)+C What is F(x)? cosx – sinx 2 2 sinx + =cos'x+cosx + =sin³x 3 3 2…

A: For ∫cos 2x-sin 2x cos 2xcos x-sin x dx=13Fx+C, to determine Fx.

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Q: Integration by Parts Example 4. Evaluate In x dv,

A: The given integral is: I=∫lnxdx   As we know that; ddxlnx=1x

Q: Consider - x2 + 2x - 10 2 (2x + 4) + 1) dx · evaluate x² (x² + 4x+ 5) (2x+ 4) +1' dx - x2 + 4x +5 x2…

A: