(1,0) (1.0) |(r? - y?) dx + 2xy dy + i | -2xy dx + (x² - y') dy (0,1) (0,1) Calculate the above integral along the given line and find a, b, c. where d is positive or negative integers Write it in the spaces below. 1.

Q: Evaluate the integral / (x" + e*) dr

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Q: Evaluate the iterated integral. 3 I (* + 5)dy dx 3 8 (x + 5)dy dx = i

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Q: (a) Evaluate the Integrals:  ∫{2x^2 + 3}/{x(x − 1)^2}dx b) Find a horizontal line y = k that…

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Q: 2. Triple Integrals For any continuous function f and constant a > 0, show that cx 1 II Fl0) dz dy…

A: Just integrate one by one.

Q: cln(2) cln(5) 2x+y dy dx Evaluate the iterated integral:

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Q: integral(integral e^(x/y) dy from x to 1)dx from 0 to 1

A: Given:

Q: Find the indefinite integral. (Use C for the constant of integratic 8 dz zV 4z2 - 25 V 4r – 25 -tan…

A: Given query is to find integration of the expression.

Q: In 4 r4 1 dy dx ex In y

A: We have to evaluate the integral                                      ∫0ln4∫ex41lnydydx The region…

Q: -4 dx Evaluate the improper integral if it exists) x2 .1 8. .2 3 .3 - 12 .4 The improper integral…

A: Since the integrand of the given integral is not defined at x=0, therefore, the given integral is an…

Q: ow that the differential form in the integral below is exact. Then evaluate the integral. 5,1) 20x…

A: We have to examine that the given differential form of intregal is exact or not .after that we have…

Q: e the Fundamental Theorem of Line Integrals to calculate F. dr exactly. F- 4 sin(4x + y)7 + sin(4x +…

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Q: 2e Consider the indefinite integral dx: (e2z + 3)* This can be transformed into a basic integral by…

A: Given,

Q: Use the Table of Integrals to evaluate the integral. (Use C for the constant of integration.) 15e30r…

A: Let, z=e15xdz=15e15xdxdx=dz15e15x Then we substitute it in the given integral…

Q: (1,0) (1,0) 1 = | (x² – y²) dx – 2 x y dy + i - 2 x y dx + (x² – y²) dy (0,1) (0,1) Calculate the…

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Q: (b) Evaluate the following integrals: (i) (sinh 2x) /1+ cosh?(x)dx, (ii)

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Q: Evaluate iterated integral.

A: Integration is the process of finding the anti-derivative function of a given function. The…

Q: S Prove that £{cos(at)} = est cos(at)dt s² + a² integrating by parts twice and the evaluation of the…

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Q: + 6) dy dx = t) Evaluate the iterated integral

A: Given,

Q: 2 - y², y = − sin (727), and Let R be the region below enclosed by the curves x = x = -1, as shown…

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Q: Find the general indefinite integral. (Use C for the constant of integration.) (x1.1 1.1 + 11x4.5)…

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Q: Evaluate the iterated integral. 1 −1 4 (x2 − y2) dy dx −4

A: We have to find the solution of double integral.

Q: Evaluate the integral.   ∫0 1/2Cos -1 x dx

A: ∫cos-1x dx=∫cos-1x·1 dx=cos-1x·∫1 dx-∫dcos-1xdx·∫1 dx dx=cos-1x·x-∫-11-x2·x dx=x cos-1x+∫x1-x2 dx…

Q: Evaluale the integral (i+2) sinz 23 dr. dz, where C: 12) =1, by any two methods and compare the…

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Q: Evaluate the integral ||| y sin x dz dy dx, where E ={(x, {(x,y,2)|0<x< xs4,0<y<1,0<zs V1- y² E You…

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Q: 9. Evaluate the improper integral: | xe* dx jze'de

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Q: Set up the definite integral required to find the area of the region between the graph of y = 17 – r…

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Q: Evaluate the integral by reversing the order of integration. 16 2 y3 dy dx + 1

A: Answer and explanation is given below

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: EX. Evaluate the oJoJ (x*+2xy+y?) dydx when step Size of X = 0-2 dnd step Size of y= o-5 use…

A: The given function fx,y=x2+2xy+y2 step size x=0.2 and y=0.5 Step size h=0.2 fx,y when x=0.2 and…

Q: dz z(z – 2)4

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Q: Evaluate the improper integral A 0 (B 4 C diverges 2 D 9 mit 2 3 -2 X 3 dx

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Q: 11-y² x 26)A) Convert the integral J Jax?+ y²)dzdxdy to an equivalent integral in -1 0 0

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Q: Q.1 Find the double integral , cos x? dA Where R between : x=-y/2, x=1 and y=-2 , y3D0.

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Q: Q4 The area between the curves y = -3 cos (z) – 3 and y = 3 cos (2) – 6 on the interval (0, 7) is:…

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Q: Express the iterated integral as an equivalent integral with the order of integration reversed.…

A: Express the iterated integral as an equivalent integral with the order of integration reversed.

Q: Which of the following integrals represents the length of the curve y = 2", 0<x < 3? 3 А. 1+ 22x dx…

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Q: Express the integral as an equivalent integral in which the z-integration is performed first, the…

A: A detailed solution is given below.

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

A: The solution is given as

Q: x € [0,2] n Q1 x € [0,2|\QS Find upper and lower Reimann integral for T(x) =

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Q: integral(integral e^(x/y) dy from x to 1)dx from 0 to 1

A: To compute the double integral.

Q: One of the correct steps to evaluate x2inx x²Inx dx to yield the correct integral A x?Inx B 1 x3 dx…

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Q: Depending on the real parameter p and q, what can you say about the result of the following im-…

A: a ∫1+∞1xpdx=limt→+∞ ∫1t1xpdx     =limt→+∞ x1-p1-p1t   =11-p limt→+∞ t1-p-1   =11-p∞  =∞

Q: Q;: Find the integral for the following functions: - 1)Sdx V-2x+1 2) ſ e3se c(x), sec(x). tan(x) dx…

A: Now integrate the given function

Q: 1_dx -1 1-x The integral is an improper integral.

A: We can find the integral as below

Q: Evaluate the line integral 11y dy over y = x for 0 < x < 3. (Use symbolic notation and fractions…

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Q: Set up the definite integral that gives the area of the shaded region bounded by the graphs of y,…

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Q: 3. Which antiderivative of y = (1 – x²)-1 should we use to evaluate the integral (1 – x²)-' dx?

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Q: 4. Express the integral as an equivalent integral with the order of integration reversed. 2√x (a) ff…

A: The process of switching between dxdy order and dydx order in double integrals is called changing…

Q: integrals in the order dædzdy 11 x2 1 | s(e;y, z)dydzdr

A: Please refer to the image below

Q: dz (x2²–x³) 1/3dx Using the substitution *=-, dx= - the integral reduces to x3 (22– 1) 1/3 -dz A) -…

A: