H(x) = V4 -f dt,

Q: Evaluate double integral.

A:

Q: Find a function f € span(1, cos x, sin x) which minimizes the integral 2πT √²* |x +1 − f(x)| ²dx.

A: Given a function                     f∈span1, cosx, sinx

Q: Determine if the improper integral converges or diverges: 1 dx. 1+x²

A: Our Aim is to determine whether the improper integral given below converges or diverges∫0∞11+x2 -(i)

Q: find integral x+1 dx 1) J T2x-x2

A:

Q: That the value of the integration g(1) = 0, g(2) = 0 1-e) -dt where g is a function that is…

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Q: 7. Evaluate using integration by parts: f Væ log, x dx.

A:

Q: Determine whether the improper integral diverges or converges. dx 1. (2х-1)3 dx 2. x +1

A: No.2 The improper integral is of second kind where f(x) = 1/(x+1) has one point of infinte…

Q: |x| dx 1 X V1– x² -1

A:

Q: Integral in REVERSE ORDER

A: Given that  I=∫08∫y32ex4dx dy Limits are given y=0 and y=8     x=y3y=x3  and x=2

Q: If the change of variables u = x -2 is used to evaluate the definite integral f(x) dx, what are the…

A:

Q: Determine whether the improper integral diverges or converges. dx 1.So (2x-1) 7 dx 2. x +1

A: We have to determine whether the improper integral ∫-17 dxx+1 diverges or converges.

Q: Evaluate the integral 2 dx where fx) if -2 s xs 0 16-2 if 0xs3

A: Given function is The integral isThe integral can be written as: Plugging the function and applying…

Q: Determine whether the improper integral diverges or converges. dx 1. (2x-1)3 7 dx 2. -1* + 1

A:

Q: If the change of the variables u=x^2-7 is used to to evaluate the definite integral upper 6 and…

A: Explanation of the answer is as follows

Q: / 2) + (2 / √x)) dx 2. ∫ ((t√t + √t) / t2) dt

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Q: If the integral diverges, indicate that using the checkbox. 6 dx The integral diverges x(x + 1)

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Q: Evaluate the integral. HINT: 3 x2 dx J2 x - 1

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Q: Let y 5x²8x + 4. If Ax = 0.1 at x = 1, use = differentials to estimate Ay Ay ~

A:

Q: Determine whether the improper integral converges or diverges

A: Given: ∫2∞ 1x-1 dx To determine: Given improper integral converges or diverges.

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

A: we have to integrate the following

Q: Integral from 1 to e of 5t^2 lnt dt

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Q: Evaluate the double integral 2. dy dx 3/x

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Q: 12. Show that F(x) = sinx – x cos x+2 is an antiderivative of f(x) = x sinx.

A: Given, F(x)=sinx-xcosx+2 To show that the above function is an antiderivative of f(x)=xsins.

Q: 6. f(x)dz = f(t)dt, If what are the bounds of integration for the first integral? = and b =

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Q: Find the general indefinite integral. (Use C for the constant of integration.) ∫3v(v2+4)2dx

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Q: d Evaluate dz 1 dt. 1+ Int

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Q: Exatuate the integral pvz O√3 √4-X² √EX 9 (√x ² + y² dy dx

A: Evaluation of double integral by conversion to polar coordinates.

Q: Use any method to evaluate the integral. 3 x*dx 2 Vx + 25 3 x*dx S- 2 Vx +25

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

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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: Set up a definite integral to find the length of the curve  y= (3/4)x(4/3) - (3/8)x(2/3) over the…

A: The given curve is,

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

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Q: x³e-x*dx 1. "Since the integral ( Select ] [ Select ]

A:

Q: If the function f(x) is defined on the 2 intervallo, TT) and f'(x) = -cos X (sinx) than f(x) has…

A: Given that fx is a function defined on an interval 0,π whose derivative f'x=-cosx1+sinx2 To find the…

Q: Let y1, y2,.., y10 be a random sample from an exponential pdf with unknown parameter A. Find the…

A: Given: y1,y2,......,y10 is a random sample from an exponential pdf with unknown parameter λ. It is…

Q: Show that integral 0 to infinity  x2 e -x2  dx = 1/2 integral 0 to infinity e -x2  dx

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Q: 3 sin 2t 1. If f (x) = Jx Ve2+Int dt, find f'(x) Jx Jt?+Int

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Q: Evaluate the integral: sinh 3x csch 3x dx coth 3x "+C 3 coth X +C 3 - coth x +C - 3 - coth 3x +C 3

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Q: Evaluate the integral S - dx V16-x2

A: Evaluate the integral of the integrand  x2/√(x2-16) .

Q: What is the reason that the integral or antiderivative always has an arbitrary constant C?

A: The integral or antiderivative always has an arbitrary constant C, because it express the general…

Q: Evaluate if the integral converges 1. 1. dx (x-1)7 , sin x dx 3. dx 2.

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Q: Evaluate the iterated double integral JI-X² ( [√x² sin (x² + y²) dz dy dx

A: A a couple of imperative is a specific imperative of a characteristic of numerous actual variables…

Q: Compute the definite integral 2 dx Vx² + 4

A: First, we need to compute ∫xx2+4dx

Q: What value of x > -1 maximizes the integral / t²(3 – t)dt?

A:

Q: Give the general antiderivative for the integrand in the definite integral (cos +1)dx. cos x

A: Simply integrate and put the limit than simplify.

Q: 4) Reverse the order of integration in 2 2x x' dydx 0 x2 and evaluate the integral as an x-simple…

A: To reverse the order of the below integration. ∫02∫x22xx3dydx

Q: State the Comparison Theorem for Improper Integrals. As well, use it to determine whether x + 2 dx…

A: For the solution follow the next step.

Q: If the change of variables u = x² +1 is used to evaluate the definite integral f(x) dx, what are the…

A: given:- u = x^2 + 1 to find:- new limits.

Q: Show complete solution Expand, that is, perform the indicated operations on the differential…

A: To expand, that is, to perform the indicated operations on the differential operator, xDD+x

Q: et * e-t Compute the convolution integral.

A: