Calculate the iterated integral. 1/2 (y + y2 cos(x)) dx dy -3Jo

Q: Evaluate the iterated integral. 8. 15 (x + y²) dx dy

A: When integrating with respect to one variable, consider other variable as constant.

Q: tan (In 4x) cos (In |(2x)"|)|+C. what is b? The integral of dx is b In A B 2 4 4

A: Given :  ∫tan(ln|4x2|)xdx=bln(|cos(ln|(2x)a|)| +C   To find : Value of b

Q: Evaluate the iterated integral below. π T/4 A lago S. 0 1 y cos (x) dy dx

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Q: Evaluate the iterated integral. 2 1T 2 - 2y3) dx dy

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Q: Question 14 1. 2 Evaluate the iterated integral. J, J. J. (x²+ y² + z?) dx dy dz -1°0 (А) 5 (в) з D)…

A: To find following integral valueI=∫-11∫02∫01(x2+y2+z2)dx.dy.dz

Q: The particular Integral for (D2 + 42)y = sin4x is. Yp

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Q: Evaluate the iterated integral. LP'&x+yaxay (x + y²) dx dy

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Q: Evaluate the iterated integral. ITT*³. /0 10 6ze-x6 dy dx dz

A: Integrate usually but first with respect to y then x then z.

Q: Find the integral [((-1)*(c+1)x+(a+1)) cos((b+1)x+(c+ 2))dx -

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Q: #1. Evaluate the iterated integrals (a) || (6x?y+4x - y) dx dy -2 (b) y2 x²y dxdy

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Q: Evaluate the integral VI- 1 /1 dy dx. – x² – y2

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Q: Evaluate the iterated integral. e² (1/xz In(z) dy dz dx

A: topic - triple integration  answer is ln(64) =6ln(2)

Q: For x 1/2 -dx and using the substitution u=x 1/2, the resulting integral takes the form: x-x 4u -du…

A: We can rewrite the given integral by using this substitution u = x1/2

Q: Evaluate the iterated integral. 8 3 (x + y²) dx dy -1/1

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Q: Calculate the iterated integral. 2 (6 7e* + 3y dx dy

A: From the given problem: I=∫02∫067ex+3ydxdy So, we can also write as: I=∫02∫067ex·e3ydxdy

Q: dx e2a +5

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Q: Calculate the iterated integral. 1/2 (y + y2 cos(x)) dx dy

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Q: Evaluate the iterated integral. 4 (x² – 2y²) dx dy %3D

A: We need to evaluate the following integral ∫12∫04x2-2y2dx dy

Q: Evaluate the iterated integral. /2 x. 4 cos (x + y + z) dz dx dy

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Q: Find the complimentary function and particular integral for (D² – 5D+6)y = e2x cos(2x).

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Q: Evaluate the iterated integral 1 ·1 dy dx (xy + 1)2

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Q: Use the method of indeterminate coefficients to find the special integral of a differential equation…

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Q: Evaluate the iterated integral. (x² – y²) dy dx -1J-2

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

A: Given,

Q: Evaluate the iterated integral. *7/3 '5 y cos(x) dy dx

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Q: evaluate the iterated integral.

A: Given, ∫-12∫0π2ysinxdx dy Now integrate above with respect to the x we get, ∫-12∫0π2ysinxdx…

Q: Evaluate the iterated integral. 2 3 4 (x² + y² + z² ) dx dy dz -2 0 0

A: ∫-22∫03∫04x2+y2+z2dxdydz

Q: (a) Evaluate the following integrals: π cos(x) dx dy 4y

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Q: Evaluate the iterated integral below. π 1 S*S'y cos (x) dy dx S. 0

A: Here we have to find given iterated integral.

Q: 2. Evaluate the following integrals. (b) § S, sin y² dy dx

A: Solution

Q: Evaluate the iterated integral Vy exp dx dy 0.

A: ∫14∫0y exydx dy = ∫14yexy0y dy                                       = ∫14ye - 1 dy…

Q: Determine the following particular integrals: -{3x²e-x} 2.1 2.2 1 D² + D-1 1 D² - D+2 {8 sin x cos…

A: To Determine: the following particular integrals:   2.1 1D2+D-13 x2 e-x 2.2  1D2-D+28 sinx cosx

Q: Evaluate the iterated integral. IT (10 + 2x2 + oy?) dx dy

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Q: Evaluate the iterated integral. 2 3y [ ?+y?) dx dy -1 0 2 3y +y?) dx dy = -1 0 (Type an exact…

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Q: iii. Find the particular integral (P.I) of y" + 9y = cos 3x

A: To find the particular integral P.I of  y''+9y=cos 3x

Q: Evaluate the iterated integral below. π/4 1 S. S'y co Só 0 0 y cos (x) dy dx

A: Solution…

Q: ...... ... ... ...- Evaluate the iterated integral. 5. y cos(x) dy dx

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Q: Calculate the iterated integral. '3 1. 7xy x2 + y2 dy dx + y2.

A: Given integration, I=∫03∫017xyx2+y2dy dx Use formulas, ∫xndx=xn+1n+1∫cfxdx=c∫fxdx   c is…

Q: Calculate the iterated integral. 5xyV x? + y? dy dx

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Q: 16–x² Choose the iterated integral that is equivalent to y dy dx in polar coordinates.

A: let x=rcosθ and y=rsinθ dydx=rdrdθydydx=r2sinθdrdθ 16-x2=yx2+y2=42=r2 r=4 Therefore r varies from 0…

Q: II cos(s5) dt ds

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Q: 1. Evaluate the integral Vi-x² ex?+y*dydx.

A: 1. The given integral is, ∫01∫01-x2ex2+y2dydx. Convert the integral into polar coordinates as…

Q: Calculate the iterated integral. (x + y)² dx dy

A: In the question we have to find integral of the given function.

Q: Evaluate the iterated integral. /3 6. y cos(x) dy dx

A: I=∫0π3∫09y cos x dy dx =∫0π3cos(x) ∫09y dy dx  =∫0π3 cos(x) y2209 dx  =∫0π3 cos(x)812 dx

Q: T/2 T/2 (b) sin(x + y) dy dx

A: Consider the given integral, ∫0π2∫0π2sinx+ydydx first, integrate with respect to dy,…

Q: Evaluate the iterated integral. 4y 18xy dz dx dy

A: The integral is ∫01∫y4y∫0x+y18xydzdxdy.

Q: Evaluate the iterated integral below. π 1 4 S*S'y cos (x) dy dx Só 0

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Q: Evaluate the iterated integral. (x² – y²) dy dx J-4

A: Given the double integrationI=∫−11∫−44(x2−y2)dydx

Q: Evaluate the iterated integral. 16 - y2 4 (x + y) dx dy

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