Find the inter val of Valiediy -2x=2 ১০) - 2.

Q: 3x+1 2-2x+2

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Q: Evaluate the integral. 4e*-³dx -12

A: Given, I=∫-1.224ex-3 dx To find : Integral value , I

Q: Find two  z  values so that  37%  of the middle area is bounded by them

A: we need to find two z values so that 37% of the middle area is bounded by them

Q: ntegrate using  u substitution

A: Our Aim is to evaluate the integral given below:-∫cos (y)1-sin (y)dy -(i)

Q: Find area of region f(x)=x2-10x+9 g(x)= -x2+8x+9

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Q: y = - x2 - 6x - 3, y = - x2 - 8x – 13, x = -5, x = -2 are bounded. Determine its area.

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Q: I, FIND HE NET AREA OF fos) - Zx and gx)= O FROM [-3,3]

A: Given : Functions f(x) = 2x and g(x) = 0   To find : Net area of f(x) and g(x) from [-3,3]?

Q: 2dy Зу-4

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Q: Evaluate the double integral: 4 LA LE 2ydydx

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Q: Why are special methods, such as l’Hôpital’s Rule, needed to evaluate indeterminate forms (as…

A: l’Hôpital’s Rule are needed to evaluate indeterminate forms

Q: The area enclosed by |3z+4y| |4r-3y| + = 3 is (where [.] denotes the greatest integer function)

A: Given: An equation 3x+4y5+4x-3y5=3. where . is the greatest integer function. To find: Area enclosed…

Q: x²dx V9-x2

A:

Q: Evaluate the integral dydx 3. 1-X 2

A: Use polar coordinates for simplification of the given integral.

Q: 4. Evaluate f VX /xVX+ 1dx using integration by algebr substitution.

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Q: Integrate from 0 to 2

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Q: F[x₁,...,n] is an integral domain.

A: Solution:-

Q: Evaluate the improper intergal 1 dxusing the residue theorem. (x2 + 9)?

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Q: Evaluate the improper intergal 1 dr using the residue theorem. (x² + 4)?

A: Solving imroper integral using residue theorem

Q: 1 .2 VX /x²+2x +3

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Q: Find the area of the region enclosed between f(x) = x² +4x + 8 and g(x) = 2x² – 1x + 2. Area = %3D

A: To find the area of the region enclosed between the curves fx=x2+4x+8 and gx=2x2-x+2, first, find…

Q: Find the betwween/bounded by area the Curue u=4y-x² and The line. 4=8-Zx.

A: Sketch the two curves From the graph, we observe that both curves intersect at x = 2 and x = 4.

Q: sketch . reverse then evaluate the inlegration 2X 2 (u x+ 2) dydx X 2

A: We have to evaluate the integral for the given region between y=x2…

Q: Evaluate the itegral by interpreting it in terms of areas. 0. 3 + 100 - x2 ) dx -10

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Q: The shaded region between the graphs of 2x2 + 20 and y = 3x – 15 is displayed - - below in orange.…

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Q: Find the integral of funcdss7 x/Snca) when ns6,7 and the intereil (15) (Gmpare the esults) by Simp…

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Q: Use trig sub. Integral from 2-3 of 1/(t^2-1)^3/2

A: We have to integrate ∫231t2-132 dt.

Q: Integrate: Show that B(p+1,q)+B(p,q+1)=B(p,q).

A:

Q: Compute ƒxz and ƒzz for ƒ(x, y, z) = xyz - x2 z + yz2.

A: Given that f(x,y,z)=xyz-x2z+yz2. We need to find : i)fxz. ii)fzz.

Q: b) Show that 2x² + 8x + 14 = 2 (x + 2)° +3 by completing the square. Hence, evaluate the integral-…

A: Use integration rules

Q: find the product of the integral 1- Sn) xy evx² dydx

A: To evaluate the double integral, first find the integral ∫0ln7yex2ydy. Consider the substitution…

Q: Evaluate the integral. 2 Ỉ -1 7t sec ¯¹t dt 2/√√3 2 7t sec¹t dt =

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Q: Find 2 pOsitive real numbers x and y such that their s um is 40 and their product is as large as…

A: SOLUTION-

Q: Evaluate the integral 4-x² ^2+/4-x²-y² 2 (x² + y² + z²)³/²dzdydx -2 J-V4-x² J2-V4-x²-y²

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Q: Evaluate the integral. 4 sec2(2t) dt 3+2 tan (2t) 2 4 sec (2t) dt%3D 3+ 2 tan (2t)

A: See the details solution in below

Q: Integrate the following using substitution rule

A:

Q: Explain what kind of bifurcation occurs at in the following systems. Your answer should be…

A: note :     As per the question we are given the following 2d dynamic system : ẋ = rx - x²   ;   ẏ…

Q: Evaluate the integral

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Q: Calculate the integral. 2x° (x + 2)²dæ

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Q: (x – 3) V 6x – x²dx -

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Q: Find the max emin, nflection Points and the in ter Vals on which the function iiHereaserdecrease…

A: Given query is to find the the key points of the function.

Q: 1. What should be A for the path independent of (2,4) xy + A 2Ay – x + xp- y? fip- (1,2) Moreover…

A: According to the given information, it is required to find the value of  so that the below integral…

Q: [x³√₁-x² 2

A: ∫x31-x2dx=∫1-x2x3dx Let 1-x2=t⇒-2xdx=dt⇒xdx=-dt2                         =-∫(1-t)tdt2=-12∫(1-t)tdt…

Q: Find two  z  values so that  42%  of the middle area is bounded by them

A: Solution: Let

Q: Integrate: dr z2 + 4z + 8

A: We will integrate the above expression.

Q: calculate x, , X2, Xg from the foloueng ノ equations using Gauss E limination method 一 3X, + X2 +…

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Q: Find the bounded by aren the a Xis and the Carve 3. X -

A: we have to find the area bounded by the y axis and the curve .