10. The region of integration D is bounded by y = 0 ,y = x² ,x = 1. Show that 1 - sin(1) xsin(y) dA = 2

Q: Q.3 Find the double integral for Sl. x2 dydx, where R between y = -4/x y = -x and x = -4

A: Ti evaluate the given double integral  first we draw  the region

Q: Evaluate the integral. er HEAD ² y³ In(x) dx, y> 0 ind

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Q: 8. Sketch the region of integration, reverse the order of integration and evaluate the integral: [T…

A: Given ∫04∫x21y3+1dydxaccording to range of integration y=x  , y=2x=0   ,   x=4 according to this…

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A: We have to use formula of Trapezoid Rule.

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Q: 1 1-xl-x²-y? Evaluate the integral S S [dz dx dy 0 0 0

A: We will evaluate the given integral in this question.

Q: 14 Find the integrals using integration by parts. a. Jx(x+ 4) dx b. JVF In Vrdx c. fr'e"dx d. [ (In…

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Q: 23) Evaluate triple integral S dz dy dx. x-y

A: Given integral is ∫02∫x22∫x-yx+ydzdydx

Q: Sketch the region of integration. 1. dx dy 1 +>

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Q: Evaluate the integral r4 pr=/2)+1 2x –- y -dx dy 2 o Jx=y/2 from Example 1 directly by integration…

A: Given,         ∫04∫x=y2x=y2+12x-y2dxdy=?

Q: Q.3 Find the double integral for Sle x² dydx, where R between y = -4/x y = -x and x = -4

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Q: . 3. Compute E y 2 z 2 dV , where E is the region bounded by x  1
y 2
z 2 and x 

A: The given curves are

Q: Solve the problem. Integrate f(x, y) = sin(x2 + y2) over the region 0<x2 +y2< 100. O T(1 - cos 100)…

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Q: 1. Evaluate the double integral of x+ 2y whose region of integration is represented below. y =1 16…

A: Consider a function f(x, y) defined at every point of the 2-dimensional finite region A Divide A…

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Q: 1. What should be A for the path independent of (2,4) xy + A 2Лу — х dy y? -dx + (1,2) Moreover…

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Q: Calculate $o (3x + 5y - cos(y)) dx + x sin(y) dy if C encloses a region of area 4.

A: To evaluate the given integral.

Q: 13. If u(x) = sin 3x and v(x) = x, what are du and dv? Writedown  u dv and  v du in this…

A: Given- ux=sin3x and vx=x To Find- The value of du and dv, write down the value of ∫udv and ∫vdu,…

Q: A// compute $(4+ e*) dx+ (siny + 3x*)dy Where c is closed bounded region lying in the first quarter…

A: See the attachment

Q: 4.) evalnate the integral dx aresinx a. WI-Y b) S x arctanx dx

A: We have to solve

Q: Solve the integral (5x - y)dx + (2x + cy)dy along the curves x = y3 from (0,0) to (1,1)

A: Explained below

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A: A cartesian coordinate system contains two mutually perpendicular number lines named x-axis and…

Q: Sketch the region of integration. "In 10 r10 1 dy dx In y

A: As y varies from y = ex to y = 10 , we see that x varies from x = 0 to x = ln 10

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

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Q: 1. Sketch the region corresponding to the double integral rx+2 dy dx x2 and reverse the order of…

A: One of the two main parts of calculus which are concerned with the study of integrals, as opposed to…

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A: Condition for line integral to be path independent is given below. ∫cFdr is path independent if F…

Q: #3. Suppose that h(x) is integrable and that ,h(x)dx=1 and S,h(t)dt = 6. Find a. Sh(x)dx b. –…

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Q: 2.2. Use numerical integration to approximate o So ysinxdydx over a rectangular region with…

A: Given integral is ∫01∫01ysinxdydx                 (1) Here f(x, y)=ysinx So f(xi, yj)=yjsinxi Since…

Q: Question included in image

A: The given integral is,

Q: 5) Sketch the region of integration and evaluate the integral x²y' dx dy

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Q: 5) Find the follow ng integrals dx 5 Sin'x cosx de JT-6x assecextany dx d)J2-x dx e) change limits…

A: Since you have posted multiple subparts question in this question so I have solved first three parts…

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A: topic - Area bounded by curves

Q: To evaluate / (3x2+ 1) In x dx using integration by parts, it is best to let A u= 3x2; dv= In x dx…

A: Integration:- A integral assigns numbers to functions in a way that describes displacement, area,…

Q: Evaluate the line integral. -y dx + x dy segment from (3, 0) to (0, 3) x2 + y2

A: Find the slope of the line through the given points.

Q: 1- f(x, y) dy dx •x+1 f(x, y) dy dx + at is the sum of the four resulting limits of integration? 3.

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Q: Sketch the region of integration and evaluate the integral || dx dy 1 y

A: The Given Integral is: ∫12∫yy2dx.dy

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A: We have to find

Q: 3 3 sin(x²) dx dy y by reversing the order of integration. With order reversed, I sin(x?) dy dx,…

A: Given:  Let I=∫03∫y3sinx2 dx dy To Find:  To evaluate the given integral by reversing the order of…

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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

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A: Substitute x1/2=y or x=y2:  ∫011-x1/2-1/2dx=∫011-y2/2-1/2dy2…

Q: 64 ans: su 3 6. Calculate the area between the Curve fcx) = x²³²_4 and the lines y=2x + 4 and y=0,…

A: area between curve

Q: 1. Find the area of the shaded region by (a) integrating with respect to x and (b) integrating with…

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Q: 2. Sketch the region of integration of the given integral Q in #1. Set up Q by reversing its order…

A: The integral is given as Q=∫01∫y2yx-ydx dy. We need to sketch the region of integration of the…

Q: Evaluate the integrals 1 (x² + y² + z²) dz dy dx 0, 0,

A: The value of the integral is, 1. The detailed solution is as follows below:

Q: # 4. Using the known areas, find the integrals. S,(1– |x|)dx b. S',[2 + /1– x²]dx а. -

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Q: 7. Sketch the region of integration, and evaluate the integral. 22л г JI * zdz d0 dr 0 л 0

A:

Q: 5. Use integration to find the exact area outside r = 4 cos 0 and r = 4 sin 0 but inside r = 2.

A: