Set up an integral for the length of the curve. y = Vi-x7, -sxs 1/4 4+ 49, 12 dx -1/4 4- 4x7 + 7x6 dx 4(1 – x7) 1/4 1/4 1/4 4- 4x7. 1912 dx 4(1 – x7) 1/4 1/4 5- 4x7 dx 1/4 V4(1 -x7)

Q: Evaluate the double integral : (y – 10x) dx | dy

A: we will integrate first inside the bracket with respect to x taking y as constant and then we will…

Q: Consider the following. x = t2 – 8t, y = t5, 1sts 4 Set up an integral that represents the length of…

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Q: Evaluate the line integral along the path C given by x = 2t, y = 4t, where 0 <ts 1. (y - x) dx +…

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Q: Set up an integral for the length of the curve. y = x°, 0 s x s 1 V1+ 25x 10 dx V1+ 5x5 dx ( V1+ 5x+…

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Q: Find the length of the following curve y = Intx + Vx - 12 on 3V2, V54

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Q: Q3/Find the value of integral along the curve C joining the points (1, 1) and (2, 3) | (12z2 – 4iz)…

A: We have to find the value of integralalong the curve C joining thepoints (1, 1) and (2, 3).

Q: Use double integral to find the average temperature of T(x. y) = 10-8r -2y

A: Temperature function is given as - Tx, y = 10-8x2-2y2Average temperature = ∬10-8x2-2y2dxdyGiven…

Q: Express the arc length of the curve y = x 4 between x = 2 and x = 6as an integral (but do not…

A: Given y=x4 between x=2 and x=6

Q: Use (a) the Trapezoidal Rule integral 1to 4    cos  2  x dx                 with n= 8

A: Given Data The integral is . The number of intervals is n=8.   The function of the given integral…

Q: express the length of the curve as an integral but do not evaluate it. r = eθ + 1, 0 ≤ θ ≤ π/2.

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Q: Explain why ƒ(x) = 0 for at least one point of (a, b) if ƒ iscontinuous and the function integral…

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Q: Calculate the integral 0∫1xf′′(x)dx if f(0)=7, f(1)=2 and f′(1)=5, where f is a twice differentiable…

A: we have to find the following definite integral. For this we can use integration by parts

Q: Evaluate the double integral: (y 8r) dr dy

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Q: Evaluate the line integral along the path C given by x = 6t, y = 24t, where 0 tS 1. (x+3y²) dy Need…

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Q: X' 2 -1 Vx * dx X,

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Q: Evaluate the line integral -ydx+ xdy along the curve C :y = 12x from (12, 12) to (0,0). NOTE: Enter…

A: In this question , we can find the given line integral.

Q: Find the integral ∫y (square root of y+2) dy

A: To find: ∫ yy+2dy

Q: Evaluate the double integral : (y° – 10x) dx| dy

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Q: Find the line integral of F along the parabola y = x² from the origin to (4, 16).

A: Using green's theorem.

Q: express the length of the curve as an integral but do not evaluate it. r = (2 − cos θ )−1, 0 ≤ θ ≤…

A: Definition used -                Length of the curve -            L=∫αβrθ2+r'(θ)2dθ

Q: Set up an integral that represents the arc length of the function y = 4x4 + 5x from the point (0,0)…

A: We have to find a, b and f(x)

Q: Set up an integral that represents the arc length of the function y = 4a4 + 5x from the point (0,0)…

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Q: sketch, reverse and evaluate the integral dy dz 15

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Q: Evaluate the line integral along the path C given by x = 2t, y = 4t, where 0 ≤ t ≤ 1. [(x + 3x²) dy

A: To evaluate: ∫C(x+3y2)dy...(1) where C is given by x=2t, y=4t⇒dy=4dt and 0≤t≤1

Q: The arc-length of the curve y= :/ Vcos(31) dt , for 0<x<- is given by which of the following…

A: For the given statement

Q: Q2/ Delermine area boundled by the curve x'+2x'y²+y%_8x°+8y= 0 t. |

A: Step:-1

Q: e following integral: 23 8xyz dz dx dy. 120

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Q: Set up an integral that represents the length of the curve. X = Vу - 9у, 1 s y <4

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Q: Set up an integral for the length of the curve. y = x°,0< xs 1 1 V1 + 6x5 dx V1 + 6x10 dx V1+ 36x10…

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Q: One of the correct. steps to evaluate x²inx. x²Inx dx to yield the correct integral (A dx x2Inx B x³…

A: The given integral,     ∫x2lnx dx

Q: Using the trapezoidal rule with n = 4, estimate the integral / (x (x+1)² dx.

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Q: Set up an integral that represents the arc length of the curve y 2xi from the point (0, 0) to (2,…

A: our objective is to setup the arc length formula

Q: Using the trapezoidal rule with n = 5, approximate the integral L' TO S³ give the error of…

A: Trapezoidal rule formula: ∫abf(x) dx=h2(y0+yn)+2(y1+y2+...+yn-1) Given ∫03dx16+x2 Here f(x)=116+x2…

Q: Evaluate the integral.   ∫0√3 arctan(1/x) dx

A: Given:∫03 tan-11x dx

Q: 1 .2 2 dx = 0 xe 0- -

A: Given: 12π∫-∞∞xe-x22dx=0   We know that; ∫eax+bdx=eax+ba+C     Note: As per Bartleby guidelines we…

Q: Set up an integral for the length of the curve. y = x°, 0 s x s 1 V1 + 25x8 dx V1 + 25x10 dx V1 +5x4…

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Q: Evaluate the integrals below: etanx sec² x 3. a) V(1 – (elanx )2 :. dx, b) / cot5x. dy

A: We need to integrate of the following integrals.

Q: Consider the curve defined by the equation y = 5x + 1x. Set up an integral that represents the…

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Q: Find the are length of the curve y² = 3x between the from x=0 to x=9 ! Use integral approximation!…

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Q: Evaluate the integral; 11 dy dx 1+ 3y3 0 vx

A: Change the order of integration

Q: Set up an integral that represents the length of the curve. = sin²(t), y = 1 –- 3 sin(t), 0 <t < T…

A: The given problem is solved below.

Q: find the integral of t sint cost dt

A: Integrand, I = t sint cost dtRecall the formula from trigonometry: sin2t = 2 sint costHence, sint…

Q: Use the Trapezoidal Rule, the Midpoint Rule, and Simpson's rule to approximate the integral In(x) dx…

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Q: Estimate the value of the definite integral + 2) dx by using the Trapezoidal Rule. (Round your final…

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Q: Evaluate the line integral along the path C given by x = 2t, y = 4t, where 0 <ts 1. Lv - x) dx +…

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Q: Set up an integral for the length of the curve. 5) y = x6, 0 s x s 1 A) V1 + 6x5 dx B) + 6x10 dx 1…

A: =&gt;ds=√(1+(dy/dx)^2 .dx

Q: V.r dx.

A: The given indefinite integral is: ∫xx-x23dx

Q: Evaluate the line integral, where Cis the given curve. (x + 6y) dx + x² dy y (6, 1) C (7, 0)

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