b = -7 6. a where a = 29 f(x) = sqrtx+7 g(x) = sqrtx+7 %3D (b) Integrating with respect to y: h(y) dy where a = and h(y) = (c) Determine the area of the region. Answer:

Q: 20. Evaluate dædy by changing the limits of integration appropriately. e y/2

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Q: Calculate (x²+y²) dx dy area when D is the limited to x²-y²=1, x²-y²= 9, xy = 2, xy=4

A: As per the question we are given a double integral over the 2d region D bounded by the following…

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A: The solution for the above equation is as shown below.

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A:

Q: Find the moment of inertia with respect to x- axis of the area between y = sin x from x = 0 and x =…

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Q: D. Use double integration to find the area of the region R enclosed by the parabola y = 4-x² and the…

A: Let's find area by using double integration.

Q: 1 dy dx 1+ y4 2. Sketch the region of integration, reverse the order of integration, and evaluate…

A:

Q: xy(y? + 1)dx + (x²y² – 2)dy = 0, y(1) = 1

A: Given: xyy2+1dx+x2y2-2dy=0, y1=1 ⇒xy3dx+xydx+x2y2dy-2dy=0 ⇒xy2ydx+xdy+xydx-2dy=0 ⇒xy2 dxy+xydx-2dy=0

Q: Q3) Reverse the order of integration and evaluate the integral 8 2 dy dx y2 +1

A:

Q: Q5A) Find volume of body from above Z = √√4x² - y² and below Z - Triple integration. 1 using

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Q: dy=(0.5x- 3) Co 3)° dx

A:

Q: Reverse the order of integration. ! f(x.y) dy dx (Type exact answers.)

A: Reverse the order of integration

Q: Q5A) Find volume of body from above Z=√√4-x² - y² and below Z = 1 using Triple integration.

A:

Q: xy dx+ (xsg'4y)dy=o suiteble integrating factor and then, exact dfferential equchoms end generel…

A:

Q: 3- show that the diff. equ. is homogeneous and Salve it (2x +34) dx +(y-x)dy = a

A: In this question we have to solve the differential equation.

Q: 2. y(2x – y + 1)dx – x(3x – 4y + 3)dy = 0

A:

Q: r6 Evaluate the integral dx dy by reversing the order of integration. NOTE: Enter the exact answer.…

A: We're going to solve

Q: The differ ential equation 2 y e =0 is b. Linear homogeneOUS d. separable

A: The differential equation is given by y4x+2y'ex = 0 To evaluate : The type of differential equation.…

Q: Q7/ Change the order of integration: 9-y f(x, y) dx dy 3 Si So

A: Order of change of integrals, according to Bartleby answering guidlines do first problem completely…

Q: Use the method discussed under "Integrating Factor found by Inspection". xy(y? + 1)dx + (x²y² – 2)dy…

A:

Q: The dimensions x and y of an object are related to its volume V by the formula V=8x^2y. How is dV/dt…

A:

Q: The area of the region between the curve y = xr? – 6x +8 and the x-axis & r = 0 ; x = 3 is given by…

A: here option c is true because we will take the area in x -axis so will take limit of x and integrate…

Q: An integrating factor for y'+8z°y = sin z is given by (a) 2z (b) In(z*) (c) z4 (d) 5e2z

A:

Q: c) Evaluate Ssin 3xcos 4x dx by using integration by part.

A: Given integral is: I=∫sin3xcos4xdx Simplifying it:…

Q: The dimensions x and y of an object are related to its volume V by the formula V=8x^2y   how is…

A: GIVEN: Volume, V = 8x2y

Q: 3- show that the diff. equ. is homogeneous and Salve it (2x+34) dx +(y-x)dy = 0

A: To solve the given differential equation

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.

A:

Q: 5. Compute the volume of the solid obtained by revolving the curve y = vx sin x about the x-axis…

A:

Q: Solve for the general solution of the given DE by using the integrating factors found by inspection.…

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Q: 1 TIy. Suppose that the The volume of a right circular cone of radius x and height y is given by V =…

A: Given that the volume of a right circular cone of radius x and height y is given by V=13πx2y and the…

Q: 2-r Change the order of integration and hence evaluate dy dx 2 + y?

A: To solve this problem. first find the region of integration by drawing the region and then change…

Q: b) Change the order of integration for So Sx - y) dxdy then evaluate it.

A:

Q: Change the order of integration of the integral ∫10 ∫y0 ƒ(x, y) dx dy.

A: Change the order of integration:Change the order of integration means to change the pattern of…

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

A:

Q: c) Evaluate Ssin 3.xcos 4x dx by using integration by part.

A: Here we have to find            ∫ sin 3x cos 4x dx Integration by parts formula is          ∫ uvdx =…

Q: 2 -πx²y. = The volume of a right circular cone of radius ï and height y is given by V 3 dy when x 4…

A:

Q: | by inspection: (3y° + xy kdx + (x°y² – 2}kty = 0 1. Integrating factors found

A:

Q: dV, where E is the region between two cylinders ²+², 5. Evaluate the integral and 2² +2²9 with 1 ≤ y…

A:

Q: Q5A) Find volume of body from above Z = √√4 - x² - y2 and below Z = 1 using Triple integration.

A: I

Q: Q3/8- Using Simpson's rule ,choose the correct integration value of x* +5 ,with width = 2? =1030…

A: By Applying Simpson's 3/8 rule.with widht =h=2

Q: 14) Change the order of integration to dx dy dz 4 4-x 4-x- y SS dz dy dx 0 0

A:

Q: I// sin(x²+y²) dV , where E is the region E = {(x, y, z) : x²+y² < 1, 0 <z< 1}. E

A:

Q: Q4- BY usin simpson rule for integration find J=Jo' e* dx. n=10

A: J=∫01e3xdx.   N=10 f(x)=e3x h=b-aN h=1-010=0.1 The value of table for x and y x 0 0.1 0.2 0.3 0.4…

Q: Evaluate the double integral: 3 +9 Lo L₂ Y COS(2 (Hint: Change the order of integration to dy dx.) y…

A: The objective is to evaluate the double integral.

Q: Use the method discussed under "Integrating Factor found by Inspection". y(x³ – y)dx – x(x³ + y)dy =…

A:

Q: Q4. a) sketch the region of integration, reverse the order of integration, and evaluate the…

A: The given integral is ∫02∫04-x2xe2y4-ydydx. The objective is to integrate the given function by…

Q: Find the total differential of z = In(x + y), x = w, y= w?. By how much will z change if w increases…

A:

Q: 3. Evaluate SIS 3z dV where E is the region inside both x² + y² + z² = 1 and z = E x² + y².

A:

Q: e-* dædy by changing the limits of integration appropriately. y/2 20. Evaluate

A: To evaluate the value of double integral.