"Definite Integrals" 1. sin | COS dr -

Q: Evaluate the following integrals using Trigonometric Substitution: 1. X-1- 16x dx

A: integration using substitution

Q: x3-1 dx J2+2x+5

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Q: Write down the gradient of the straight line represented by the equation y = −0.05t + 47. What does…

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Q: Show that - 8. ==1+* +4++++1=

A: We know ∑1n2=π26  Hence, ∑1(2n)2+∑1(2n+1)2=π26 Therefore, 14∑1n2+∑1(2n+1)2=π26 ∑1(2n+1)2=π26 - π224…

Q: Describe all absolute extreme points of P. Select the correct choice below and, if necessary, fill…

A: Let's find.

Q: Suppose z is a function of x and y, and tan Vy? +x² = ze6y. Solve for and dx ду

A: Here, given that z is a function of x and y and tan y2+x2=zxe6y⇒tan y2+x2=ex ln ze6y...(1)

Q: '9 — х? dx x2

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Q: x = -2t 1- y = z – 8 and l2 2 - 3 Given: line lı : 4 y = 2 + 2t % = 6 + 2t 2. Find the equation of a…

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Q: _4. What is the area of the enclosed regions in problem number 3? A. 10 sq. units B. 12 sq. units C.…

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Q: Find an implicit and an explicit solution of the given initial-value problem. dy y – 1 dx x? - 1'…

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Q: -dx x2 +9 I x3 +ar-23 ton- (특) +C a. 3 b. 1 x³ t qx + 27 tam " ) + C b*3-9*+27€an )+c C. d.늘-9x- 2구…

A: Using substitution method, integration is done.

Q: ²+² +1) d + a (a – 2y) dy = 0 %3D

A: Given problem:- Find the solution of the given differential equation:  (x² + y² + 1) dx + x (x - 2y)…

Q: derivatives power series

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Q: cal | a*(a³ + 3)/4 dx. (+3)/4 dx. 4

A: integration

Q: 1 (s+1)(s2 +1) + cos t - sin t) + cos t – sin t) O Option 4 O Option 2 5(e-cost + sin t) 5(-e+cos t…

A: L-1{ 1/(s2 +1)(s+1)} expand it  L-1 {-s/2(s2+1) + 1/2(s2 +1) + 1/2(s+1)} L-1 s/(s2+1) = cos(t) L-1…

Q: Find the vector of length v7 in the direction of AB + AC

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Q: 4. Find (a) the gradient of f at P and (b) the rate of change of the function value in the direction…

A: A detailed solution is given below.

Q: Find the producers' surplus at a price level of p= $57 for the price-supply equation below. p= S(x)…

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Q: x2 - x 1+ 3x? – 2x3

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: Use a calculator to find the approximate value of the expression. Round the answer to two decimal…

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Q: 3s + 2 4s2 + 12s + 9 3 4 + 4 stet 3 2 Option 1 Option 2 3 2 4 + tet 4 3 2 Option 3 Option 4 None of…

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Q: dx 4x2 -8x + a a. S そ m 14cx-0+51+ s5 tom'/22 4 -2 b. I m1a(x-1)"+51-55 toni" )+c Ciln14 Cx-1)+sl+…

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Q: 3. Evaluate the integral / Vr+3 (x- 1 4 4 (a) 극(z +3)72-(r + 3)52 + 국(2 +3)%2 +C 1 4 (b) (r + 3)"…

A: This question is related to Indefinite integration, we will solve it using given information.

Q: 3 4 11) –3 0 -5 Ans. r = 2 - 4 5

A: A detailed solution is given below.

Q: - «) lim (2 – ez x→0

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Q: the

A: We have to choose the correct option from the given options according to the given information

Q: 8x? -x t 8 x (x² + 4) 9. b.4mx4 3m (x+4-ラ4an)tc c. qlnxf 6m (x"+4)-Arctan )t c d. 2mxt 6m Ge?+4) -…

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Q: e problems y' + e = 0, y(0) = 1 %3D

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Q: (c) Let f(x) = In(x + 8). (i) Find the domain and range of the function. (ii) Find the inverse of…

A: Let's find.

Q: Find f5(x) if f(x)= 3√3x+2

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Q: dx Vx-4x-7 S- -dy y2-8y+5

A: The given integrals are' 1)1/sqrt(x2-4x-7)  2)7/(y2-8y+5).

Q: 2eln In cos 2t 8 + 2 None of the choices Option 2 2s s2 – 2 s2 – 2 Option 5 Option 3

A: This question is based on Laplace transform.

Q: set D: Problem #G Find the eauation OF the Iine tangent to F Cx) = cos? x - Sin? (x) at X 3r %3D 4

A: To find the equation of the tangent line at x=3pi/4.

Q: tan x - dx 2 sec x – tan x 2.

A: Topic:- integration

Q: dx Vx²-4x-7

A: According to the company rule, we can answer the first question and rest can be reposted.

Q: dz f1-42-223)2 3 4[3-2(2+パ) a. In 3+ JE (z+1)/ J3-2(241=+C 3-4,(2+)? 3 b. 4[3-2(2+1=)] C-A(24)?…

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Q: Use the Linear Approximation to estimate Af for f(x) = when a = 2 and Ax = 5+x2 (Use decimal…

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Q: 2. Determine a•5 for each of the following a) å = (7, -3,5)andb = (-5,11, -2) 3. Determine the angle…

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Q: sove the focowing using Lagrange Multiptiers: Maximi ze flx, Y, 2) solaject to x2 + y + 22 =1 Ax +…

A: Method of Lagrange Multipliers : 1.) Solve the system of equations .…

Q: xチ+1=4 DIDX= 2-2y (ost) X= 3サ-3 *キーに h で3,0) サ=2メー オー×ポーカ toノー4) メッとナ+ム メーリー3

A: Explanation of the answer is as follows

Q: Use (a) bisection method and (b) false position method to find the solution to the following within…

A: Note: There are multiple questions. Few questions has multiple subparts.No specific question has…

Q: f 3p2tanip dp

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Q: SIn(5 + VT)dr Algebraic Substitution

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Q: IV. Problem Solving: A. Write the expression as a single Integral 1. '= xp(x)fJ + *P(x)f = xp(x)f f…

A: As per policy only first three questions are answered. Please refer to the image below

Q: Expand and simplifyW – 35) · (5 + 2w)

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Q: Find the length of the curve r(t) = (e* cos t, et sin t , et), – In 4 <t<0.

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Q: Q3. (a) Find the binomial expansion of (1 – x)-1 up to and including the term in x2.

A: We have to find binomial expansion.

Q: dx 5x2 + 16

A: Given that a integration and we find the solution of this question by general formula of the…

Q: What is the farthest point on the sphere x2 + y2 + z2 = 16 from the point (2

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Q: Question 6 Use differentials to find the approximate value of y: (2x 1) when x = 0.98. O (E) None of…

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