Use Gaussian Quadrature (n = 3) to approximate f(x)dx, where: f(x) = (2.54 - sin0.32x)2 cos0.32x , a=-1 & b= 1. 1/2

Q: dx Perform the Integrations 1+ sin x+ cos x

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Q: Find the value df (a) that Make ECX) is Contincity at X- Ž

A: Given that :f(x)=cosx2x-π      ,             x≠012a2-3a+4      ,   x=0

Q: The linear approximation at x 0 to sin(2x) is A + Bx

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Q: Given: y = x - sin(2x) Find: dy dx 0 - cos²x 2 ○ - sin² x 01+ cos²x O sin²2 X

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Q: Use the trapezoidal rule with n = 5 to approximate 3 cos(x) -dx Keep at least 2 decimal places…

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Q: Evaluate cos √6x dx using a substitution followed by integration by parts.

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Q: find dy/dx by implicit differentiation. 3cos(8x)sin(7y)=8

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Q: use the chain rule to find: 28) dv 2- COSxy + y cos x

A: Solution:Given   z= cos xy+ y cos xx=u2+v and y=u-v2To find :dzdvFormula:ddx(cos x)=-sin…

Q: Estimate S, cos(4x)dx with Trapezoidal Rule. n = 10

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Q: Find the local linear approximation of cos x at xo = cos 61°. T/3 and use it to approximate

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Q: Use the trapezoidal rule withn = 4 to approximate 5 cos(x) -dx- Keep at least 2 decimal places…

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Q: Determine the constants a and b such that                                                       sin…

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Q: Find the slope of the curve 2xy = In(e*) sin(x) at the point (2,2)

A: to find the slope differentiate  the equation with respect to x .

Q: If y = √√1-x² sin¹¹x, prove that (1-x²)+xy=1-x². dx

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Q: sin(2t)dt 0,

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Q: TT sin 5. Approximate dx by Simpson's rule with seventh ordinates?

A: Simpson's Rule:    ∫abf(x)dx=∆x3f(x0)+4f(x1)+2f(x2)+...+2f(xn-2)+4(fn-1)+f(xn) Where, ∆x=b-an We…

Q: The approximation of I cos (x²+5) dx using simple Simpson's rule is:

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Q: Integrate this item using (parabolic) Simpson's rule, with interval width of 2.00 units. x tan x + 5…

A: The formula for Simpson's rule isSn=∆x3f(x0)+4f(x1)+2f(x2)+4f(x3)+...+4f(xn-1)+f(xn) where…

Q: Evaluate 1 ei sin x cosx dx using Simpson rule with h = 20

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Q: in integrating the function fx cos() dx using intogration by parts, whut would you choose for your…

A: Solution

Q: arctanx e dx (1+x²,"

A: The given problem is to evaluate the given integral. We have to evaluate by using substitution…

Q: Use the first two non- zero terms to estimate ∫​sin(x^2)dx from 0 to 1.

A: Solution:- Use the first two non-zero terms to estimate ∫01sinx2dx

Q: c) Use trigonometric substitution to integrate dx 4-x2

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Q: Ni cos(2?)a. Cos | x dx

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Q: Use the trapezoidal rule withn = 5 to approximate 4 cos(x) -dx

A: To approximate : ∫14cosxxdx using Trapezoidal rule with n=5

Q: Estimate 1 7 cos(x2) dx 0 using the Trapezoidal Rule and the Midpoint Rule, each with n = 4. (Round…

A: I=∫017 cos (x2) dx             f(x)=7 cos (x2)b=1, a=0, n=4h=b-an=14=0.25aThe Trapezoidal…

Q: Find dy/dx in terms of x and y if arctan (x^3)=xy^3?

A: To find the derivative of the given function.

Q: A particle, initially at rest, moves along the x-axis such that its acceleration at time t > 0 is…

A: Given acceleration, a(t)=cost,       t>0 And v(0)=0, x(0)=3

Q: Use the trapezoidal rule withn = 5 to approximate %3D 5 cos(x) dx Keep at least 2 decimal places…

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Q: Use the Errors in the Trapezoidal Rule and Simpson's Rule cos(4nx) dx

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Q: f cos² x dx

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Q: In integrating the function fx cos(3x) dx using integration by parts, what would be your du? du = x…

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Q: The antiderivative of the function sin (Gx+7) is:

A: Given : sin12x+7

Q: (a) Determine f 2xe3*dx by using integration by parts. (b) Determine S cos(x²) 2x dx by using…

A: Given,  ∫2xe3xdx ; We have to integrate using integration by parts ∫cosx22xdx ; We have to…

Q: In integrating the function fx cos(3x) dx using integration by parts, what would be your v?

A: Solution

Q: Use integration by parts to find, x cos2x dx 프2

A: Consider the given integral which is required to solve using integration by parts.

Q: Use the composite trapezoidal rule with the step length h = 0.1 to evaluate sin x = 5.² in six…

A: Given integral is ∫0πsinxxdx. We have to evaluate the given integral by using composite trapezoidal…

Q: In integrating the function f(3x + 5)(cos) dx using integration by parts, what would be your v? v =…

A: The integration by parts is done using the formula: ∫udv=uv-∫vdu. In general, the ILATE rule is used…

Q: Use the trapezoidal rule with n = 8 to approximate cos(x) -dx Keep at least 2 decimal places…

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Q: f sin-¹(x) dx

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Q: Q2 \ Evaluate .1 dx by using trapezoidal rule. 1+x2

A: See the details solution in below

Q: Evaluate / e*cos(x)dx using integration by parts-

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Q: Use the trapezoidal rule withn= 4 to approximate cos(x) dx Keep at least 2 decimal places accuracy…

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Q: Find the trigonometric integral ∫sin2(x/2)  dx

A: From the given data:

Q: Consider the implicit function. ev = sin (2x) dy in terms of x. dx Determine the formula for dy dx

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Q: Use Euler's method (with all details) to find approximate value of = 2y - 2x² -3, given that y = 2…

A: Given: y'=2y-2x2-3 , y(0)=2 , h=0.3. We find y(3) by using Euler's method. The formula for Euler's…

Q: proximation at z = 0 to sin(4r) is A + Bx where A is:

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Q: Use a linear approximation of f(x)=cos(x) at x=5π/4 to approximate cos(222∘)

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Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: