Q/Use Definitien 13.4-1 +o prove that f(x,r}>x+y' is difterentialeat (o,0).

Q: Compute or show divergence: 1 а. dx 3 Vx+1

A: In this question, the concept of integration is applied. Integration Integration is a method of…

Q: Show that the differential form in the integral is exact. Then evaluate the integral. (1,2,3) Jazy…

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Q: Evaluate the integral. (Use C for the constant of integration.) / test at

A: We have to use byparts formula

Q: ag Use the Chain Rule to evaluate the partial derivative at the point (r, 0) = (2/2, 7) where g(x,…

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Q: ln (ale) secx (2– sec²x)em sec(3A – x) What should be the value of A for dr to be integrable using…

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Q: Find the average value of f(x) = sin³ x cos³x on the interval [0,1].

A: We need to find average value.

Q: ) Use integration by parts to verify the reduction cosxsin x n-1 Scos" xdx=!

A: Here I=∫cosndx ⇒I=∫cosn-1x×cosx dx using integration by part;

Q: Evaluate using integration by parts: fx sec-¹x dx

A: SOLUTION-

Q: (a) Evaluate the indefinite integral (anti-derivative) d.x Vr2 +1 by using the substitution u = x?…

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Q: Compute for the value of constant (C) by solving the given DE using integrable combination. Let x=2,…

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Q: Compute for the value of constant (C) by solving the given DE using integrable combination. Let x=1,…

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Q: Find F'(x), where F(x)= int. of ((t^2)+1)dt, from sin(3x) to x=-4. Use the 1st rule of the…

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Q: Use integration by parts to prove the reductionformula.

A: Consider the following integration by parts formula: ∫uvdx=u∫vdx-∫dudx∫vdxdx ILATE Rule: We have two…

Q: Use integration by parts to prove the reductionformula.

A: Concept: The calculus helps in understanding the changes between values that are related by a…

Q: What is the integrable form of et dx? e-e-X

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Q: Q2. Give a counterexample about a bounded function that is not Riemann integrable.

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Q: Find the maximum and intlection points between X =0 and 2T tor the curve /2-s Sin X

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Q: S Vtan x sec“(x)dx Evaluate the integral a

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

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

A: we have to integrate the following

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: Compute for the value of constant (C) by solving the given DE using integrable combination. Let x=1,…

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Q: Prove that div curl v = 0 where the components of v have continuous second partial derivatives

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Q: integral of sqrt(9-x^2)(x)dx. limits are from 0 to 3

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Q: Verify the integration formulas in Exercises 37–40. sech x dx = tan'(sinh x) + C 37. a. sech x dx =…

A: Hey, since there are multiple questions posted, we will answer the first question. If you want any…

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

A: Given

Q: R; Being the 1st region of the coordinate plane between the y = x line and the y=x² parabola,…

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Q: Determine whether the statement is true or false. If f has continuous partial derivatives of all…

A: since curl of divergence i.e

Q: dx 1 Vx + x3

A: Answer

Q: Find F '(x). F(x) = integral of 2/(x+8) dt in interval [x^2,0]

A: Let u=x^2 Then du/dx=2x

Q: show that uuX)-X (1+x*J% I'sasolutionto integralequation ux)=X-sinh (x-t)u (t) dt

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Q: Is the function f(x) = ( 1, x not equal 1)             ( 0, x equal 1) integrable over the interval…

A: Here, we will show that the given function is integrable. Let us take a point c ∈ (0,1).

Q: (5)Obtain the integral curve for x 2+y = x passing through the point

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Q: The second order partial derivative of f with respect to z (mean fz) where f(x, y, z) = x'0 sin(3y +…

A: Given: fx,y,z=x10 sin3y+10z To determine: fzz

Q: * Using integration by parts, the integral sec³dx is equal to 1 1 - secxtanx +In|secx +tanx| + C 2 1…

A: Use by parts method of integration

Q: Show that the integral is independent of the path, and use th Fundamental Theorem of Line Integrals…

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Q: Compute for the value of constant (C) by solving the given DE using integrable combination. Let x=1,…

A: We will find out the required solution.

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

A: Option 2 will be correct choice.

Q: Derive the error term of composite trapezoidal rule for integrating S f(x)dx.

A: ok, let us say that we are dividing this region in n regions,

Q: Compute the partial derivatives: z = sinh(r²y^) az ||

A: We will find out the required values.

Q: Express the limit as a definite integral on the given interv * 2x, + (x;")² Ax, [4, 8] lim n- 00 i =…

A: Given that: limn→∞∑i=1n2xi*+(xi*)2∆x,   [4, 8]

Q: Inx F (x) = So It dt %3D

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Q: ar Let = 2x - 1. Integrate this partial derivative with respect to x, letting h(y) be an unknown…

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Q: Find the limits of integration with respect to u and v

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Q: Solve using integrable combination technique only: (x^2y^3−(6+1)y)dx+(x^3y^2+(9+1)x)dy=0

A: Solve using integrable combination technique only: (x^2y^3−(6+1)y)dx+(x^3y^2+(9+1)x)dy=0

Q: Find dq/ ər if q = x' + xy² where x = 2r, y = r² In(r + m cos r), and z = 3. Show the correct…

A: given q=xy+xyz   ...i where x=2ry=r2lnr+mcosrz=3 to find- ∂q∂r

Q: isolated singular point 1. z/((z^3)+z) 2. exp(tan(1/z)) 3. (1/(z^2)) * exp(1/(z^2)) z=4 is apole of…

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Q: Svaluate x dx from the definition of RS-integral.

A:

Riemann Sum

Riemann Sums is a special type of approximation of the area under a curve by dividing it into multiple simple shapes like rectangles or trapezoids and is used in integrals when finite sums are involved. Figuring out the area of a curve is complex hence this method makes it simple. Usually, we take the help of different integration methods for this purpose. This is one of the major parts of integral calculus. 

Riemann Integral

Bernhard Riemann's integral was the first systematic description of the integral of a function on an interval in the branch of mathematics known as real analysis.