1. Evaluate the integral r4-x² 8x cos Y dy dx Y – 4 by reversing the order of integration.

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 by reversing the order of integration of S. xe y dydx хе у b) c) 0 d) None of these 1/2

A: The given integral is ∫0∞∫0x xe-x2ydy dx. We need to evaluate the integral by changing the order of…

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

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Q: 10. Evaluate the integral ffS (xy + z²)dV, where E = {(x,y, z:0 Sx< 2,0 < ys 1,0 <z< 3)} using three…

A: given , integral ∫∫∫xy+z2dV  where E=x,y,z:0≤x≤2,0≤y≤1,0≤z≤3 claim- to evaluate the integral

Q: Evaluate the iterated integral. 2y (2 + 4x² + 8y²) dx dy 0 Jy

A: To evaluate:∫02∫y2y2+4x2+8y2dxdy

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: E ralu ate the given ヤyle integral: S. x² rin dy dz dx

A: Given that, The integration is, ∫0π∫0x∫0xzx2siny dy dz dx We have to find the value of this…

Q: 3 The triple integral L (x + 2y – z)dxdydz is equal to

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Q: Let I = [ -1 y+x y-19y+xª dxdy. By reversing the order of integration of I, we get: Osysx^2+1…

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Q: B- Evaluate the following double integrals: .2 .4 1) | (x+ 3y x²)dy dx

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Evaluate the double integral: To L 0 y x7 +1 y¹/3 x7 dx dy.

A: The given integral is: I=∫08∫y132yx7+1dxdy   So, The limit of the x varies from y13 to 2. The limit…

Q: Evaluate the iterated integral. 2y (10 + 2x2 + 6y²) dx dy 0 Jy

A: The given integral is: I=∫02∫y2y 10+2x2+6y2 dx dy

Q: Evaluate the iterated integral. (x² – y²) dy dx -1J-4

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Q: 1. Reverse the order of integration on the following double integral. f(x,y) dy dx A. y) dx dy B. y)…

A: Given: ∫14∫1xf(x, y) dydx

Q: c3 2x 7. Consider the double integral f(x, y) dy dx. Set up an equivalent double integral by…

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Q: 1. Evaluate the following integrals (mixture of integration techniques). (a) /e's y² +8y- 3 sin 0 de…

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Q: Evaluate each of the following partial integrals. 1. 2 co e*sinydxdy 2. (x + 2xy - 3y?)dydx II. 2e…

A: It is partial integral

Q: (a) Calculate the iterated integral 3 7/2 SS(v+y° cos x)dx dy -3 0

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Q: 2. Reverse the order of integration and then evaluate. o S x² sin(xy)dxdy a.

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Q: 1)Calculate the following double integrals. (y + xy-2)dA, where R = {(x, y) E R²/ 0 < x < 2, 1 < y <…

A: Solution:

Q: What is the integrating factor of the non-exact DE (4xy+3y² – x)dx + x(x+2y)dy =0 ? 2 (A 2 B x2 1 x2

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

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Q: Evaluate the iterated integral.

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Q: 14 Find the integrals using integration by parts. xp_ († +x)xf • - dx c. fr'e"de e flnx'de d. f (in…

A: Solution: The objective is to find the value of the given integral

Q: Evaluate the integral ſ xe²" dx; * dx; u=x, dv= e²ª dx using integration by parts with the indicated…

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Q: Compute the following integrals. 1 t3 (a) dt. Jo V4+ t² (b) e6x cos (3e2) dx. (Hint: you might need…

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Q: What is the integrating factor of the non-exact DE (4xy+3y² – x)dx+x(x+2 y)dy =0 ? 1 A x2 B x2 2

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

A: ∫-22∫03∫04x2+y2+z2dxdydz

Q: (b) Evaluate the following integrals: z²+cosz (i) [ezsiniz) + + sin22]dz, C: |z| = counterclockwise.…

A: (i) Given integral is∮Cezsinz+z2+coszz10+sin2zz2dzC: z=π2 counterclockwise.The integral is evaluated…

Q: 1- Evaluate the following double integral using Ax = Ay = 0.5, and Trapezoidal Rule of Integration.…

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Q: 39.: * Compute the integral: x (Inx) dx. a. (5e –1) b. (3e -1) c. (e +2) d. (5e -e') (e* -e) 32 16…

A: Use by parts integration

Q: 3. ( ) The integral f S, sin(y²)dydr cannot be evaluated since f sin(y³)dy is not an elementary…

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Q: 4. Reverse the order of integration and evaluate the integral: -8 () La dy dx 20° sin zy dy da (a)…

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Q: %3D 7. Evaluate the following integrals using the multiple rule of integration take (Ax = Ay = 1):…

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

A: Given: I=∫-11∫-44x2-y2dydx   As we know that; The Power rule; ∫xndx=xn+1n+1+C

Q: (b ) [. SS. 1 dx dy dz xyz

A: Given ∫1e∫1e∫1e1xyzdx dy dz

Q: 3. Evaluate Sy In(1+ y) dy using integration by algebraic substitution.

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Q: ]] x² + y² 1+ y² dx dy

A: We have to evaluate the integral ∬x2+y21+y2dxdy, Where D:0≤x≤y≤1 Here, limit of x is 0≤x≤y And limit…

Q: 6. How would you begin to numerically approximate the double integral: bd 1-SSS(x.y)dxdy ac

A: Given integral is   I=∫ab∫cd fx, y dx dy

Q: 12

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Q: Use the Table of Integrals to evaluate the integral. (Use C for the constant of integration.) YV 6 +…

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Q: 4. Evaluate the double integral: LL y x² +1 (Hint: Change the order of integration to dy dx.) dx dy.

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Q: 15. Evaluate the integral ſo S, x²y² dy dx (a) directly, (b) integrating with respect to x first and…

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

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Q: If H is the integrating factor of 6xy dx + 5(x² + y)dy= 0, then compute H(8). A 1 в) 2

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Q: 2. Evaluate the following Integral by using suitable method: 2y3 + y y4 + y2 + 1 dy -

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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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Q: b) Evaluate the triple integral S dx dy dz re3 1 xyz

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Q: 4. Evaluate the double integral: Y SS² ¹/3 27 (Hint: Change the order of integration to dy dx.) dr…

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