5. Find the particular integral of d²y + dy - x2 + 2x + 4 dx2 dx

Q: Evaluate the double integral. LL. 3 (x² – xy2) dy dx -3

A: first, we integrate with respect to y

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

A:

Q: Evaluate the iterated integral. 5 4 (3x + 5y) dx dy 5 4 (3х + 5у) dx dy %3 i

A:

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

A:

Q: Evaluate the improper iterated integral. x2 dy dx 1 + y2

A: Given: I=∫03∫0∞ x21+y2dydx As we know that; ∫11+x2dx=tan-1x+C And ∫a·fxdx=a·∫fxdx, where a is…

Q: Evaluate the integral 1 2 s s хе dx dy -1

A:

Q: Evaluate the integrals in ∫2y dy/y2 - 25

A: Given integral:

Q: Evaluate the iterated integral. •2Vx + 1 (xy + 7)dy dx 2vx

A:

Q: Evaluate the integrals: x² dx (x-1)(x²+2x+1) -dx 1. S 2. S x²+2x x4-3x²-4

A: Here we have to find the integral.

Q: 1. Find a particular integral for d²y dy dr +4- + 3y = r? dr2

A:

Q: Evaluate the given integral 2x +3 -dx- (x + 1) (x – 1)²

A: Integration formulas help to integrate the given fuction. Simplification of the function helps to…

Q: Evaluate the iterated integral. 74 (x² - 2y²) dx dy

A: Given that a double integral we solve this integration by using general property of integration.…

Q: Evaluate the iterated integral. 21 4 (x2 – 2y2) dx dy

A: We need to evaluate the following iterated integral ∫12∫04x2-2y2dxdy

Q: Evaluate the integral. In3 3e2x dx In3 3e 2x dx = 0

A: As we know that; ∫a·fxdx=a·∫fxdx And ∫eaxdx=eaxa+C From the given problem: I=∫0ln33e2xdx

Q: Evaluate the iterated integral. 9. (8x – 2y) dy dx 1

A:

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: 3. Evaluate the following improper integral; -2 2 dx x² – 1

A:

Q: 4. Compute the following integrals. 2 2x2 + 18 dx. x3 – 3x2 (a) - x3 + x2 + 4 (b) dx. x5 + 8x3 + 16x

A:

Q: evaluate the iterated integral.

A: ∫03∫-20x2y-2xy dy dx=∫03∫-20yx2-2x dy dx=∫03x2-2x dx∫-20y dy

Q: Find a particular integral for d^2y/dx^2+ 4dy/dx+ 3y = x^2

A: We have to find particular integar

Q: Evaluate the double integral. y dy dx O - 3x

A:

Q: Consider the following two improper integrals: (1) 1 dx г — 5 -1.7 dx (2) (x –

A:

Q: Compute the double integral ff(6zy2 +12z³y + 4y) dx dy with R= 3,5 z [1,2].

A: See this solution in below.

Q: Evaluate the double integral : 9. dy dx 0, 22

A:

Q: So S(x + 3) dy dx 3. Evaluate the double integral:

A:

Q: iSy dx dy 3.

A:

Q: Evaluate the integral. S yz dx dz dy 0 2 2 O 128 3

A:

Q: 1. Evaluate the followng integrals dx b)S5x-2 dx

A: We have to evaluate the integrals. a). ∫1x+xdxb). ∫5x-2x2+1dx

Q: Evaluate the iterated integral. 4 1 (3x – 5y) dy dx -1

A: We need to evaluate the value of the following iterated integral ∫14∫-113x-5ydydx

Q: Evaluate the integral: 1. - 1 (1- 5x + x³ – 2x5 5х + x3 — 2x5 dx x2 2. S(y³ – 3,/y+ Vy) dy

A:

Q: 3. Evaluate the integrals. dx ( Use u = Vx(1+x)

A:

Q: Evaluate the iterated integral. (3x - 2y) dy dx 1 Jo

A:

Q: Evaluate the iterated integral of 2 2x . (x2 + 2y) dy dx

A: Evaluate the double integral

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

A: Given problem:-

Q: Evaluate the iterated integral. 3 4 5 /// + x² + z² ) dx dy dz -3 0 0 3 4 5 !! (x² + y² + z² )dx dy…

A: We have to find

Q: Evaluate the integral.

A: We have to evaluate the integral: ∫x3xx2+3y2dy Here we have to integrate with respect to y so x2…

Q: show y=3x+cos3x is a particular integral to d^2y/dx^2 + 3dy/dx +2y = 6x-7cos3x-9sin3x+9

A: To show: y(x)=3x+cos3x is a particular integral to d2ydx2+3dydx+2y=6x-7cos3x-9sin3x+9.

Q: Evaluate the integral; 11 dy dx 1+ 3y3 0 vx

A: Change the order of integration

Q: 1 uate the improper integral dx. x(In x)3

A:

Q: Evaluate the iterated integral. (8x – 2y) dy dx

A:

Q: Evaluate the iterated integral. (x2 - 8y2) dx dy

A:

Q: Solve the problem. Rewrite the integral 5(1 - z/6) 2(1- y/5 - z/6) dx dy dz in the order dz dy dx.

A:

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: Evaluate the double integral dy dx 31x

A:

Q: In Evaluate the integral: Sé e x²+3x-7 x-2 dx

A: Option (b) x22+5x+3ln|x-2|+C

Q: Find the partial integral. (3х + 5y) dx

A:

Q: 2 Evaluate the iterated integrals. 2 (x + 3) dy dx 0, 6. y sin x dy dx

A:

Q: Find the integral. 5x* dx (5+x*)* 1 O A. 3(5+x)3 OA. 1 О в. В. +C 5(5+x*)5 Oc. (5+x)°. +C

A: