mcory amu LAampIOS 45. Finding an upper limit of an iterated integral Solve for a: 1-x² ¢4-x²-y 4 dz dy dx = 15

Q: d) 1) Explain why the following integrals are considered as improper integral. Then re-write the…

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Q: a) Use the Simpson's rule to approximate the following integral x Inx dx.where n 6 b) Find the bound…

A: The integration of the function can be approximated using the Simpsons rule. The formula for the…

Q: Using Simpson's (1/3) rule with h = 1, evaluate the integral: I 7 ·S= 3 x² logx dx

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Q: a) Evaluate x In (2.x) dx by using integration by parts b) Find the area bounded by the curve x- 3+…

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Q: Suppose the curve y = f(x) passes through the origin and the point (1,1). Find the value of the…

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Q: Evaluate the iterated integral. 1 13 4ze x* dy dx dz

A: The given integral is: I=∫12∫01∫0x3 4ze-x4 dy dx dz

Q: If - 1 | f(2)dr = | f(x)dæ + / f(=)dr - /. f(æ)dx, what are the bounds of integration for the first…

A: I have used the properties of integration

Q: 5 Given Ln 3 + (i 4 + (i – 1). , express the limit as m → ∞ as a n n n definite integral, that is…

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Q: e dx . If the integral converges enter the exact value of the integral. If the Evaluate lo (ez – 1)²…

A: Solution:- The given improper integral is  ∫01ex(ex-1)2dx  we have to prove that; the given integral…

Q: y + 2 "hat is the indefinite integral of JC² - 1)(² + 1 )" dy ? 2 (y² – 1) (x² + 1

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Q: dx The integral can be re- 1-x A lim (-1+ 2 V1–m ) - 00 B lim (2 – 2 V1-m ) 1–m ) m -- 00 lim (- 2 +…

A: We have to choose the correct option according to the given options

Q: If f(x)dr f(x)dæ + f(x)dx – what are the bounds of integration for the first integral? a = and b =

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Q: 1. TⓇ S (a) Find the general indefinite integral. 2t² + t²√t-1 t² dt

A: topic- definite integral

Q: 3. Evaluate the iterates integral: SL(x-y) dy dx

A: We have to solve

Q: integral SS₁₁) dx dy xy=1, y = x, x=2 Calculate the in D limiteel to

A: An integral is a mathematical object that can be interpreted as an area or a generalization of an…

Q: Naluate integral foin+c)dt 3.

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Q: The improper integral e-3x dx 0. equals Refer: improper integral O 1 O 1/3

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Q: 00 1 Evaluate the improper integral 1 dy dx as an iterated integral. x³y 2 e-X The value is

A: We apply first integration on y then on x

Q: I don't understant this hw problem

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Q: 6.3.28. Evaluate the integral. using U substitution integrate (x^2)sqrt(x^2-1)dx

A: Use substitution method, to evaluate the integral

Q: (4+ysin(y)-3^/y²` dy. Find the general indefinite integral f y

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Q: edx e dx (e*+1)*

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Q: 00 2 10) Evaluate the improper integral dx. Use limits as needed 8

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Q: 2) Evaluate the integral. T/2 L cot³x dx

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Q: YA y= f(x) -2 2 4 6. 8 Evaluate the following integrals by interpreting them in terms of areas: 2…

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Q: (c) Does Ihe de finile integral for Ihe function f(x)= Cosu JI- Sinx for Ihe limits o to I Conver…

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Q: dx integralini hesaplayınız. x(In x)

A: Fundamental theorem allows us to compute definite integrals using the antiderivatives. It states…

Q: y = f(x) 2 3 Area=5 Find the definite integral | 2f (x)dx =?

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Q: 304² 3x Evaluate dx dy, by first Reversing the order of integrals. √36 + x3 Enter an integer or a…

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Q: I.Evaluate the ff. iterated integrals. n |4 2 sin x cycosx y dz dy dx Jo

A: To evaluate the given triple integral.

Q: Evaluate the iterated integral. 8 1 (3х — 9у) dy dx - Exact number, no tolerance. 8 (Зх — 9у) dy dx…

A: Given:      ∫18∫-113x-9ydydx     =∫18∫-113x-9ydydx integrate with respect to y…

Q: 1 2. Evaluate the integral using integration by parts. Hints: LIATE, 은(cos-1(x)) : dx 1-x² cos-(x)…

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Q: a) Evaluate the Integrals: 2x2 + 3 x(x + 1)2 b) Find a horizontal line y = k that divides the area…

A: (a) part Consider the given integral ∫2x2+3xx+12dx Now,…

Q: -. Express lin (we (2 4 ) - 2 (2 + 2)) 2 2+ as a definite integral, f sec n→∞ N i=1

A: Given  limn→∞3n∑i=1nsec2+3in-22+3in

Q: Evaluate the iterated integral. (2х — 4у) dy dx Exact number, no tolerance. (2x – 4y) dy dx = i -1

A: The given integral is: I=∫111∫-11(2x-4y) dy dx

Q: dx The integral can be rewritten as VT - x 00 lim (-2+ v1– 3) S--00 lim (-1+2v1– s) s--00 B lim (-2+…

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Q: If - 2 f(x)dæ f(x)dx + f(2)dæ – / f(x)dx, what are the bounds of integration for the first integral?…

A: We have to solve the integration

Q: 25 3. In r If the triple integral fo So So (xe") dydr dz Find the upper limit value E.

A: We have to find the value of E.

Q: If g(1) = –1, g(5) = –8, and g(a) dx -9, evaluate the integral æg'(x) dx. %3D

A: Given g(1)=-1, g(5)=-5 and ∫15g(x)dx=-9

Q: 1 c) (x² + e#)% ( Hint for part (c): Try to use Comparison Theorem for Improper Integrals) -d.x

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Q: If 3 7 f(æ)dæ | f(æ)dæ - f(a)dæ, what are the bounds of integration for the first integral? a = and

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Q: 25 20 15 10 5 ol 1 2 3 4 5 * a. Approximate , g(x)dx using the area of the rectangles in the image.…

A: According to questionWe have to calculate the approximate area.

Q: السؤال 8 Evaluate the improper integral if it exists e'dx: - 00 -e.1 O e.2 O .3 0 The improper…

A: We will evaluate the integral and check if it converges.

Q: Solve the problem. Rewrite the integral 5(1 - z/6) 2(1- y/5 - z/6) dx dy dz in the order dz dy dx.

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Q: Set up the definite integral that gives the area of the region. Y1 = x2 – 5x Y2 = 0 dx 3 * 4 6 12,…

A: Area of the Region bounded by the curves :If f(x) and g(x) are two continuous function on a,b and…

Q: IE < (b - a)3 12n2 -[max |f"(x)|], a < x s b Trapezoidal Rule |El s (b - a)5 180n4 [max |f(4)(x)|],…

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Q: Question : evaluate the following iterated integrals CLE dy dx

A: In the given iterated integral first we integrate with respect to 'y' and after putting limit of 'y'…

Q: 00 dx Evaluate the improper integral if it exists 1.10 The improper integral diverges 20 2.3O 6.40

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Q: x+y xydx dz dy Jo

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Q: + oo Consider the improper integral dx . What will be an appropriate solution and answer? x2+ 2x+ 2…

A: We have to find solution of improper integral.