Consider / sin'x cos²x dx. jf we let " =cos x , the integrand can be transformed to , O J(- 2u?- u* +u®) du A B None of the choices | (u²+ 2u+ +u°). O - /(u?- 2u* + u°) du (2и2+ и4 — иб) du

Q: If D is the region enclosed by y = , x = -3, and y= 0, then: II.-96y° dA =1. Select one: O True O…

A: Given problem:-

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Q: x² + 64 Using trigonometric substitution, given - dx, the simplified form of the integral is: (sec…

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Q: 1 Solve the integral: 1+x + C + C C) None of the given choices 5. Inl + C 56

A: Let's find.

Q: Vx² –25 The antiderivative of dx is x2-25- sec lx+C. A) True B False

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A: We can solve this problem as follows:

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A: The given integral,         ∫-40∫03y+14y dxdy

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A: In this question we have to find the derivative of the given function.

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A: Given problem:- If a ball is given a push so that it has an initial velocity of 24 ft/sec down a…

Q: Write T if the statement is true, or F if it is false. W. 1. -dx x' +C 3 %3D 45x=-5x +C 9. 2. %3D 4…

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Q: 1 Y(s) : s2 + 7s + 10 a. y(t) =(e-5t – e24) b. y(t) =(e-5t + e²') c. y(t) =(e5t - e-2t) d. y(t)…

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Q: Find the derivative of f(x) = x In(x) 1- In(x) O In(x) O1+ In(x) O In(x) /x

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Q: In each of the problems, solve the given differential equation. 1. y` = 1 + x + y2 + xy2 2. y` =…

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Q: y" + 4y" + 4y' = 0. %3D

A: Follow the procedure given below.

Q: Find the absolute extrema of the function on the closed interval. y = 4 cos x, [0, 27] Step 1 The…

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Q: In fx³Vx²-62 625 dx , if we let x = 25sece , then dx =25secede. True False

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Q: f(-1,–5)= f(-5,–1)= f(0, 0)= f(5, –5)= f(t, 2t)= f(uu, и — v)-

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Q: Set up, but do not evaluate, an integral for the surface area of the surface generated when the…

A: writing given function as x in terms of y

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Q: If ở x w = i- j+ k, and v · w = 4, and 0 is the angle between v and w, then (a) tan 0 (b) ө

A: (a)v×w =i-j+k|v×w| =12+(-1)2+12=3|v×w| =3|v×w| =|v| |w| sinθ →(1)now,v.w =|v| |w| cosθ →(2)(1)(2)⇒…

Q: Work Problem 1 (With integrity statement] Let R be the region bounded by yx+ 2, y=0, und x=2. Draw…

A: To find the value of given double integral.

Q: (a) Find the unit vector having the same direction as B- A+ 2C. (b) Give the direction angles of B-…

A: We have to solve given vector Questions

Q: 1 In solving the antiderivative of f(x) = 3sin(x) + 4cos(x)+ 5 by miscellaneous substitution, the…

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Q: Let R be the region bounded by y =x+4, y=0, and x=4. Draw the region R, and evaluate the following…

A: Let's find.

Q: y" – 1/x = 0; y = x In x – 5x + 7 -

A: This question can be solved using the concept of first and second order derivatives.

Q: x = 2y X=y-8 -12 12 -8-

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Q: The position of a particle in the xy-plane t time t is r(t) = (e') i+ i. Find an equation in x and y…

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Q: x2 In solving for the antiderivative of f(x) = [4-x² using trigonometric substitution, Jf(x)dx is…

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Q: d d Calculate [ri(t) · r2(t)] and r1(t) × r2(t)] first by differentiating dt dt the product directly…

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Q: Determine whether Rolle's Theorem can be applied to f on the closed interval [a, b]. (Select all…

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Q: dz In Vz+4 - 2 2ydy , if we let y=Vz+4, then the new integral becomes у-2 A True B False

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Q: Ql Find Ax

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Q: 2x + 1 -d.x J (3x – 1) (x² + 2.x + 2)' Evaluate:

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Q: Evaluate the integral. (Use C for the constant of integration.) 10 dx 5x + x/x

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Q: Sy+1-2dy can dy = 4x(x²+2)dx. be evaluated conveniently if we let x VVy+1-2 and True False

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Q: I. Evaluate the triple integral zdV, where E is bounded by the cylinder y? + z? = 16 and the planes…

A: Let's find.

Q: In solving the antiderivative of (x)= sin(x) + 3cos(x) + 3 by miscellaneous substitution, the…

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A: Use first substitution then use integration by part

Q: (2х+3) dx (x2+3х-6)9

A: ∫2x+3(x2+3x-6)9dx=∫(x2+3x-6)-9 (2x+3) dxusing formula∫fn(x) f'(x)dx =fn+1(x)n+1+chere, f(x)=x2+3x-6…

Q: Solve the following Initial Value Problem: y"+ 16y 0, x)= 2 and y'() = 5. %3D

A: Topic = Differential equation

Q: Consider / sinºx cos?x dx. |f we let u=cos x , the integrand can be transformed to A / (u²+ 2u+ +…

A: topic - indefinite integral

Q: Question 8 In |x³Vx2 – 625 dx , if we let x = 25sece , then dx = 25secede. True F False

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Q: S sin®xdx

A: ∫sin6x dx       We have sin2 x=1-cos2x2 Then ∫sin6x dx=∫sin2 x3dx                  =∫1-cos 2x23dx…

Q: •4 b (3x – 4)° dx = || f(u) du where (enter a function of x) = n dx (enter a function of x) — пр a =…

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Q: Brd Derivative OF y=-Jin3x

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