Find ao of the function f(x) = (T -x)2 n^ 2/6 5π. 2/12 I ^ 2/12 Ο 5πλ2/6

Q: Find the Integration of: fn (3sint + esin t) cost dt In 3

A: Given that, ⇒                   y =∫π2π( 3sint +esint) costln3dt⇒                     find the value…

Q: What is the maximum value of y = cos x. For - < x < < ?? 1 1/2 2.

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Q: Find the maximum and minimum valucs of f(x) = sin x + cos x on (0, 2n].

A: Given function:                      f(x) = sin x + cos x,   x∈[0, 2π] Use the second derivative…

Q: Find all critical points of the function: R(θ) = cos θ + sin2 θ

A: The derivative is defined as the rate of change of one quantity with respect to another. In order to…

Q: What value of b &gt; -1 maximizes the integral function

A: Given,

Q: Kim throws a ball against a wall at time t = 0. At time t = 1, it hits the wall and then at time t =…

A: The objective here is to check whether Mean Value Theorem can be applied to show that at some point…

Q: Show that f(x) = sin x (1 + cos x) is maximum when x = Hence find its maximum value.

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Q: Evaluate the qwen Detinite Integra ax(7-x²)* dx 2X

A: From the given integration: I=∫-3-22x7-x23dx.....(1) Using the substitution method to calculate the…

Q: Determine of y = cos(x) – V5a2 In x.

A: I have stated the used formulas in the solution.

Q: 3G)Ú) Show that the reduction formula for atanx で-u sec"x dx = Sec" 「キu ) Hence use tthe formula to…

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Q: The maximum value of y = sin x, 0 &lt;= x &lt;= 2p, isand occurs at x =__________ .

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Q: Q3. Show that дхду for дудх f = x² siny – 2y³ cos2x (

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Q: Issol za 53. f(x) = VxIn x on (0, co) %3D

A: Given: 53.   fx=xlnx,  0,∞

Q: 4) Use integration by parts to find f x² In 5x dx

A: As per our guidelines we need to solve only one question.please, repost the remaining questions as…

Q: A scientist uses the one-point Gauss quadrature rule based on getting exact results of integration…

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Q: aresin (2x-1) = 1-x 2 arctan

A: Substitute x = cos^2(theta) and simplify the equation.

Q: Evaluate the integral. 1//3 3earctan(y) dy -V3 1 + y2

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Q: dx - Evaluate V4x' +9

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Q: The integration expression sin(3In(x)+ 4)cos(3ln(x)+ 4)dx must be transformed into using suitable…

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Q: Find the CRITICAL VALUES of f(x)=sin² x+cosx on the interval (0,2n)

A: Critical points are the points where the derivative of the function is zero or undefined. Our…

Q: Find the integral of * dx 2 sin x – cos x - |tan + 2 + v5 + C tan + 2- V5 In | tan + 2+ v5 |tan + 2…

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Q: Find the Integration of: f(3sin t + esin ty cost dt In 3

A: we have to integrate the following

Q: 5) What is the maximum value of y = 5 Cos 4x ?

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Q: 1) sinh-1x = In(x + Vx² + 1) %3D 2) cosh-1 x = In(x+ Vx² – 1) %3D 3) tanh-1x In ) X = 1-x

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Q: Evaluate the integrals ∫(sec2 x) etan x dx

A: Evaluate: ∫sec2xetanxdx

Q: I need to integrate 1/(sqrt(a^2+x^2)). If I let t=x+sqrt(x^2+a^2) where t&gt;0, then how do I…

A: The given integral is,

Q: Let u = x3 + 1. Indicate how the limits of integration should be adjusted in order to perform the…

A: Given

Q: Integrate the function. 2+81 dx 4x2 V In Vx2 + 81 + x x2+81 4x + C In Vx2 • 81 + x] Vx2 + 81 + C 4x…

A: Given,            ∫x2 + 814x2 dx

Q: he integra = 3/2 is dz Z-2

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Q: In² xdx

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Q: FInd the length of the curve y= 2ln ( sin(x/2)) from x = π/5 to x = π

A: Formula to find the length of the curve is  ∫ab1+dydx2dxGiven y=2ln(sinx2) Lets find out dy/dx by…

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

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Q: -f integration for

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Q: What is the value of the function xcosnxdx if we integrate it using Kronecker' smethod?

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Q: Find the area of a triangle bounded by lines y=2x and x=1 by double integration

A: Given region, y=2x        ...(1)x = 1        ...(2) Substitute the value of x = 1 in (1), y = 2 So…

Q: Limit _π/2 toπ/2 integral (1+cosx) dx

A: To integrate: ∫-π2π21+cosxdx Solution: Property of definite integral states that: ∫-aafxdx=2∫0afxif…

Q: 13. To evaluate f 2costx-1 dx, the integrand can be transformed to 1-sin²x a. [(3cos³x+csc²x)dx b.…

A: Here we have to transformed the given integrand.

Q: Evaluate: S 0 tan¬(0)d0 arctan(8)–0 Sarctan 0 + C 2 arctan(0) 0 zarctan 0 + C 2 arctan 0- 0…

A: Please refer the attached image for complete solution.

Q: Find the linearization of ƒ(x) = sqrt(x + 1) + sin x at x = 0. How is it related to the individual…

A: To determine the linearization of the function at x=0.

Q: find the most general antiderivative of f(x)= 2x^3 - sinx + 4e^x

A: We find the integral of f(x)= 2x^3 - sinx + 4e^x We separate the integral first.

Q: Find the area of a triangle bounded by lines y=2x and x=1 by single integration

A: A definite integral can be used to compute area bounded by curves. If there are two curves f,g over…

Q: Find the absolute extrema of the function on the closed interval. y = 9 cos x, [о, 2л] (x, y)…

A: Given,

Q: Find the the Yegion bounded by area y= tanx 4

A: integration gives the area of any function y .

Q: Use integration by parts to evaluate (2x + 1)e2-1dx.

A:

Q: What is the Fourier transform of the one-dimensional rect function rect(x) = 1, for |x| |x|…

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Q: 2. f x cos² x dx

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Q: Calculate using integration by parts: x^3 sin(x^2) dx

A: Given: ∫x3sinx2dx

Q: 6) csch-1x = In Vx2+1 (+ sinh-11 %3D |x|

A: 6. First  we will find relation between csch-1x and sinh-11x. From Hyperbolic trigonometric…