Use geometry to calculate (without integrating): o V16 – x2 dx Note that f (x) = v16 – x² is the top semicircle of radius 4.

Q: b) Change the order of integration for . S(x- Jy=o Jx3xy) dxdy then evaluate it. |

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A: Given: x+y=9+x2y2

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A: Find your answer below

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A: Intregation of product of two variables is given below

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A: Topic = Differential equation

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A: ∫t2+t2 dt

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Q: Integrate the following using substitution. You must show work. 7y(v² + 7)°dy

A: We have to find the definite integral using substitution method In place y^2 =t                2y dy…

Q: Write the general antiderivative. (Use C for the constant of integration.) x2+1 dx 5x Need Help?…

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A: Given equation  y=A+be^x Where A & b are arbitrary constant.

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A: The given equation is: xy=2+x2y

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

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Q: S e6m sin m dm Integration by Parts

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A: We have function f(x,y)=x+x2y, y0=1, and h=0.1. We have to use the Runge-Kutta method to find an…

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Q: Q1/ Evaluate the integral: -За (2уах 3a dy dx x2 4a by changing the order of integration.

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Q: Solve the DE using homogenous equations: Let: x = vy dx = vdy+ydv xy dx - (x2+3y2) dy = 0

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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…

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Q: (a) Integrate the following function; i) SG) dx 1+9x² ii) S dx (b) Differentiate y = cosh-1(x² + 1)…

A: 5(a) (i) Given integral is ∫91+9x2dx ∫91+9x2dx=9∫1919+x2dx=∫119+x2dx=∫1132+x2dx Hence,…

Q: Find the total differential. w = eбy cos(4x) + z7 dw (No Response)

A: Explanation of the answer is as follows

Q: Obtain the solution using Integrating Factors Found by Inspection. 1. ydx + 2(y* – x)dy = 0

A: As per our guidelines we can answer only 1 question. So kindly repost the remaining questions…

Q: Find work done from the followingW = G- sec²(3x)- V8) dx witch Gx +9 h used to stretch a spring from…

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Q: Q 4. a) Use integration by parts to evaluate Sz²cos zdz. b) Evaluate f xlog(x + 3)dx.

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Q: Evaluate xe dx (x + 1)² using integration by parts. [Hint: f(x) = xe“, g(x) = (x +

A: ∫xex(x+1)2dx

Q: Find a solution to the SDE dX; = X,(ydX; + tdt), where y ER is a constant and Xo = 1.

A: The given equation is dXt=XtγdXt+tdt. The given initial condition is X0=1. The integration formula…

Q: Q3) Evaluate triple integral (x2-y?)dz dy dx.

A: Introduction: When the integrand is a function of three independent variables, we use triple…

Q: Find the value(s) of dy at y=1 given that x²y+y² =5. dx only only D

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Q: [[ dx dy Q4 )Evaluate by changing the order of integration

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Q: find the integration of f x'e* dx

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Q: Express in form y=f(x) by eleminating the parameter x = ln t , y = 2 − t

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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.

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Q: dy Given that y = In 9x, find dz dy

A: Use derivative rules to find dy/dx

Q: Using the substitution x = sec 0, dx S: J x2Vx2 _ 1 where x > 1, is equal to

A: We can find the answer as below.

Q: b) f(x): 1 + sec2

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Q: Find the most general antiderivative of f(x)=6e^x+5 sec^2(x), where -pi/2

A: Please see the answer below

Q: Integrate dy (a) y'Jy? +16 6. (b) V6x Vox-x* dx –

A: Hello. Since your question has multiple parts, we will solve first question for you. If you want…

Q: -2x 11/E valuate the integral 2 é V1-

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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: Obtain the solution using Integrating Factors Found by Inspection 1. ydx + 2(y* – x)dy = 0

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Q: Q2) Evaluate , S2 xsiny? dy dx 0 Jx2

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Q: The radius r and height h of a right circular cylinder arerelated to the cylinder’s volume V by the…

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Q: The antiderivative of [Vx²-25 dx is x2 – 25 – sec-lx+ C. A True B) False

A: ∫x2-25xdx

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A: To evaluate the value of double integral.