Find a curve through the origin in the xy- plane whose length is given by 1/2 L = [; (1+ *)"* dx 4

Q: The surface area of a sphere, initially zero, increases uniformly at the rate of 4 xq.in. per sec…

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Q: the in integra a) (x³ + 1)dx

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

Q: Set up the integral for the arc lengthof the function,y=4/3x^3/2for 2≤x≤6if you integrate with…

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Q: Show that ∫0∞ e-x 2 dx = ∫10√(-ln y)  dy  by interpreting theintegrals as areas.

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Q: Estimate | (2x – 5) dx using left endpoints for n = 3 approximating rectangles. %3D 5 (2x – 5) dx is…

A: Given: ∫152x-5ddx The left Riemann sum (also known as the left endpoint approximation) uses the left…

Q: How large should we take in order to guarantee that the Trapezoidaland Midpoint Rule approximations…

A: Given

Q: The error is numerically computing the integral | 1 dx using the +4 trapezoidal rule with two…

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Q: Find a definite integral that represents the arc length. r = 8sec(θ) on the interval 0 ≤ θ ≤ π/3

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Q: Estimate (2x – 5) dx using right endpoints for n = 3 approximating rectangles. (2x – 5) dx is…

A: We have to estimate the , ∫15(2x-5)dx using right end points for n=3

Q: dx 4.Exaluate I=| correct to three decimal places by Trapezoidal rule with h=0-25.

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Q: Find the length of the curve y=ln(sec(x)), 0≤x≤π/4.

A: please see the explanation below

Q: Use the Trapezoidal Rule to estimate the integral |dx using n = 4. What n is needed for 2 decimals…

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Q: Write down an integral expressing the length of the curve y = cos x, 2 2

A: Apply the below formula: L=∫ab1+dydx2dx

Q: Set up the integral for the arc lengthof the function,y=4/3x^3/2 for 2≤x≤6 if you integrate with…

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Q: Calculate the left rectangle approximation of 3x- dx using five subintervals.

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Q: Find the length of the curve y = ln(sec(x)), where 0 is less than or equal to x which is less than…

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Q: Use a linear approximation (or differentials) to estimate the given number to the nearest hundredth.…

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Q: Approximate - -1x+3 -dx using trapezoidal rule with n=4 and Simpson's rule with n=4.

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Q: Find the length of the arc of x2 + y2 = 64 from x = -1 to x = -3, in the second quadrant. (Solve…

A: We need to find arc length.

Q: nd the points at which f(x) = cos² x has a horizontal tangent line. %3D

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Q: Use the Midpoint Rule with n = 4 to approximate 2x the integral 1 dx to three decimal place.

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Q: (a) Use the Midpoint Rule with n = 6 to approximate integral 8 x-6 S8 dx 6 x+8 ?

A: As per the instruction, we will be answering the first question. Given:

Q: Find the equation of the line tangent to the cardioid r = 1+ sin(0) at Ô0 =

A: Given that,, Here, differentiate w.r.t. ,we get, We know that, To find: equation of the line…

Q: Express the arc length of the curve y = x4 between x = 2 and x = 6 as an integral (but do not…

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Q: Find the area of the loop of the curve y2=x3 (1-x)6. Show complete solution of points of…

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Q: What is the equation of the curve whose tangent line passes through the point sec? (In x) dx ? (1,2)…

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Q: Use the trapezium rule to find [2" dx taking ordinates with interval 0.25, in three decimal places.

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Q: Use Simpson's Rule with n = 4 steps to estimate the integral. 42) | 7 dx 1+X

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Q: Find the area in the first quadrant bounded by the curve Y = 4–?^2 and the axes using horizontal…

A: Consider the region bounded by the the curve and the axes in the first quadrant

Q: integral from -1 to 1 of arccos (y) dy

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Q: express the length of the curve as an integral but do not evaluate it. r = sin3 θ, 0≤ θ ≤ 2π

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Q: solve: d/dx on the intergral 2x to x3 with an integrand of t2 et^5 dt

A: Given integral is

Q: Find the derivative dydx of the function x=arctanet, y=1+e2t at t=0.

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Q: Use the Midpoint Rule to approximate the integral 13 | (- 2x + 10æ²) dx with n=3.

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Q: Evaluate the integral (8 (8x+15y)dx + (27x - y)dy along the parabolic arc y = x² from (0,0) to…

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Q: MY N nd the minimum value of n that guarantees an error of no more than 1/30,000 in approximating -…

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Q: THE AREA BETWEEN THE CURVES 4 y = x²³² AND y ²³ = 4X IS REVOLED 2 ABOUT THE LINE X= -1. SOLVE FOR…

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Q: Use the composite trapezoidal and Simpson's rules with step length h = 0.4 to estimate In(2+3/x)…

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

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Q: Use the Midpoint Rule with n = 4 to approximate the integral. 10 x² dx M4 =

A: The given integral is ∫210x2dx. The mid point rule states that if fxis continuous on [a,b][. Let n…

Q: An area is bounded by the x^2+10y-1600 curve  and the -xaxis. Find the moment of inertia (in units4)…

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Q: 2. Use the Midpoint Rule with n = 4 to estimate (x² + 1) dx %3D

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Q: Find the minimum value of n that guarantees an error of no more than 1/30,000 in approximating the…

A: Given the integral: Hence we have

Q: Determine the equation of the tangent line to the graph of g(x) = Sm, [1 – sin(ne')]dt at %3D In x…

A: We have to find the equation of the tangent line to the graph of gx=∫lnx01-sinπetdt at the point…

Q: .find the integral by Gamma fun y(-Iny)5 dy

A: Gamma function is defined as Γ(x)=∫0∞xn-1e-x dx .               Disclaimer: Since you have asked…

Q: Use the Midpoint Rule with n = 4 to approximate the integral. %3D 14 x2 dx

A: We have to solve the integration using mid point rule.

Q: Use the Trapezoidal Rule with n = 4 to approximate the value of: +1)dx.

A: Given,  ∫12x3+1dx, n=4

Q: Use the Trapezoidal Rule withn=4 steps to estimate the integral. 3 16) dx Use Simpson's Rule with n…

A: 1.  According to the Trapezoid rule,…

Q: The minimum value of n required to approximate xe dx by composite Trapezoidal rule with an error…

A: Find the minimum value of n required to approximate ∫02xe-xdx by composite Trapezoidal rule with and…

Q: The definite integral that can be used to find the arc length of the curve y =x-2 on the interval…

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