Solve the triple integral I| (x² + y² + z²)7/2 dV where B is the unit ball B O 2n 2л О Зл 5 o 7n 5 O o

Q: Evaluate the integral fa* (2* – 11)"dz, dx, by making the appropriate substitution: u = 11). 24 dx =…

A: ∫x3x4-1124dxSubstitute u=x4-11du=4x3dxdu4=x3dx

Q: Q2. Evalnate the double integral SS хе ク over the finite regieon 2 R={(x)): x2, y54ーx3

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Q: Calculate the double integral. /| 10(1 + x). 1+ y? dA, R = {(x, y) | 0sxs 3, 0 sys 1} %3!

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Q: 7. Evaluate the integral (16 – 2? – y?) dV where E is the solid hemisphere x² + y² + z² 0

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Q: 15. Evaluate the double integral (a + 6y? + bx²y) dA, where R = {(x, y) E R² : |x| + \y| < 1}.

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Q: Use symmetry to evaluate the double integral. 4xy 1+ x2 dA, R= {(x, Y) | -4 s x s 4,0 s y s 1}

A: When the upper and lower limits of definite integrals become same, the result is zero irrespective…

Q: Evaluate the triple integral of (1 − x2 − y2) dV, where H is the solid hemisphere x2 + y2 + z2 ≤ 4,…

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Q: Find the complete integral and singular integral of z = px + qy+√√1+p²+q²

A: Given partial differential equation is z=px+qy+1+p2+q2. We have to find the complete integral and…

Q: Consider the indefinite integral r523 + 2х? — 72х-32 2x2 – 72x dx 16 - Then the integrand decomposes…

A: Evaluate definite integral ∫5x3+2x2-72x-32x2-16dx

Q: Evaluate the integral: r+∞ 1 dv v²+2v-3

A: We will find the integral.

Q: Consider the triple integral I = S S“(y² – 6z)dydzdx. -

A: ∫02∫x21∫0xzy2-6zdydzdx=∫02∫x21z3x33-6z2xdzdx=∫02x31-x812-6x13-x63dx=31.88888…

Q: Calculate the integral f. (z-2)²2 dz, where C: |z – 1| = 3.

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Q: Evaluate the triple integral. II y av, where E {(x, y, z) | 0 s x s 5, 0 s y s x, x - y szS x + y}

A: Here, we have to evaluate the triple integral

Q: Apply Green's Theorem to evaluate the integral P (3y2 dx + 3x2 dy), where C is the triangle bounded…

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Q: In (rle) sec³x (2– sec²x)«ma/2)sec³x What should be the value of A for dx to be integrable using the…

A: we have to find the value of A.

Q: Evaluate the integrals in Exercises 7. (x² + y² + z²) dz dy dx 0 J0

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Q: 9. Evaluate the integral // V2 + y² + z² – 3 dV where S lies between a² + y² +2² = 1 and a? + y² +…

A: Given integral, ∭sx2+y2+z2-3dV Where S lies between x2+y2+z2=1 and x2+y2+z2=9. The spherical…

Q: Evaluate the double integral. /| 6xy2 dA, D is enclosed by x = 0 and x = V4 – y-

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Q: Apply Cauchy integral formula to find the value of the integral ſ. AG-DE dz; where C: |z| = 3. 2z-1

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Q: Consider the indefinite integral + 222 – 29z – 21 da. 1² – 9 The integrand decomposes into the form…

A: Let's find.

Q: Calculate the double integral. 3xy2 dA, R = {(x, y) | 0 s x< 1, -2 s y s 2} x2 + 1

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Q: 5. Evaluate the double integral (a + 3x + bry) dA, where R= {(x, y) E R² : |x|+ |y| 0 and b > 0).

A: To Evaluate: ∬Ra+3x2+bxydA, whereR=x,y∈ℝ2:x+y≤1

Q: ne following integral 2dr J r (3(ln r)2 + 12 In z- 15)

A:

Q: Evaluate the iterated integral. 7 8 (x² + y² + z²) dx dy dz -6 0 0 7 8 (x² + y² + z² )dx dy dz =

A: Given that: ∫-66∫07∫08(x2+y2+z2)dxdydz

Q: Estimate the double integral_R  (3xy^(2)+2x^(2)) dA where R= [0,1] x [0,1] by diving R into four…

A: We need to evaluate integral.

Q: Apply Green's Theorem to evaluate the integral (4y² dx + 4x² dy), where C is the triangle bounded by…

A:

Q: Qi (a) Compute the multiple integrals of (i) V4-z xy dxdydz (ii) (1) , (8 – x2 –- y²)dA, where R =…

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

Q: 3z+4 dr Use the appropriate substitution to evaluate the following integrals: e %3D O e3a+4 + C ©…

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Q: Q.2. Calculate the integral of: f(x) = (3x+1) from a=-0.2 to b=0.6 by using Simpson's Rules only and…

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Q: Q.5 Evaluate the integral with the aid of the formulas 5,6, and 7. dt V9-4t2

A: We have to solve integration .

Q: Finel the integraL of finchio XSina) wher ne 5 and (0,2) by Simpsors rule 3.

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Q: Evaluate the double integral. бу dA, 2x5 + 1 D = {(x, y) | 0 <x< 1, 0 < y s x²}

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Q: Evaluate the triple integral and confirm that 2 2 dx dy dz = = In 35, where D is the rectangular box…

A: We will prove the given statement .

Q: 2. Evaluate the integral 8- (a) L« (4t5/2 – 3t3/2) dt (d) 2 - Vt dt r4 (e) t2 cos e de JT/4

A: The objective is to find the values of given integrals

Q: B D cF I| f(x, y, z) dV = dz d

A: We have to evaluate the integral:

Q: Find the integral. 5. S(2ri+j+k)dt 6. sec' ti+- -jdt 1+r

A:

Q: The value of the improper integral / 36 z² e ² dz = 12e1 O - 36e 1 O 36e 1 O 12e 1

A: We need to evaluate the value of the following integral I = ∫1∞36x2e-x3dx

Q: The value of the double integral 32 dæ dy is O- 1536 O 1536 O 3072 -3072

A:

Q: 3-Evaluate the integrals in Exercises: 2√3 So dx √4 + 4 + x² 0 4- 6 dx 5. Sot v Jo V1 + 9x² cos x dx…

A: We have to evaluate the integrals.

Q: d.x (a) Evaluate the integral ; x In(4x) using the substitution u = In(4x). dx J r In(4x) +C -7x (b)…

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Q: 2_ Calculate the generalized integral. x In r dx J. (1+12)3

A: The given integral: Calculate the above integral:

Q: Compute the integral VI-y² In(a? + y? + 1)dædy 1-y² y=-1 Jr= and enter the solution below with up to…

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Q: The value of the triple integral (x² + y²)dV where E is the E portion of x² + y² + z² = 4 with 0 ≤ y…

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Q: Q.1 Evaluate the given integrals using part I of the Fundamental Theorem of Calculus. [3 Marks] i.…

A: You need to find the integral of the given functions using the fundamental theorem of integration.

Q: Evaluate the integral. I (2i + t/t - 6j + t sin(zt)k )dt J6

A: Given:

Q: Compute the double integral f[148 sin( + ) oyck, where R = {(x,y) /0 5x s %,0 sy s }. х, 3J. R OA…

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Q: What is the value of the integral (3z-2) with respect to z from z=-i to z=? 0 a -i b 1 .c O -1 i…

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Q: Evaluate the integral fos√²²-1 f√²-1. 2x by first rewriting in the order dxdy. Enter the numerical…

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Q: Evaluate the triple integral [[Scosys3 12xy²z³ dV_over the rectangular box G define by the in…

A: We have to find value of given triple Integral.