dr? What is the integrable form of et-e A (1-u²) ² du O fa- B 2 du 2 du 2 du 1.

Q: •2 1 -dx- J-3 (x + 7)(x² + 16)

A: Given integral is Apply partial fractions to break the denominator

Q: Evaluate (423 + 3y? + 2z)dV B = {(x, y, z) | 0 < æ < 3,0 < y < 2,0 < z< 2} .

A:

Q: A fair coin is tossed two times independently. Let H₁ = {1₁ (1, if head is obtained at the ith toss…

A: When head is obtained at 1st toss then H1= 1  When head is not obtained at 1st toss then  H1= 0 When…

Q: Clear my choice 4x + 11 dx %3D 11 +c 2x2 4x 11 +c 2a6 4 O 4r + О 4 2x2 11 +c 2x2 4x + 11 +c 6x2 4x +

A: we need to integrate the given function ∫4x3+11x3dx

Q: Evaluate " " So s L dz dx dy rvZ c3y (8-x²-y² Jx²+3y²

A:

Q: Find 4rye®y? dA, where R [0, 1] × [0, 2]. R

A: The objective is to find the double integration where  R=[0,1]×[0,2]

Q: 1. Find 2(3z + 4)² dz.

A:

Q: EVALUATE Sx csc(2x) cot(2x) dx A. -z csc (2r) +in esc (2r) - cot (2-)| + C В. B. z csc (2z) + In…

A:

Q: P4: x3 (x² + 1)3

A: Use the algebraic substitution and solve the integration.

Q: Compute dx. X + 2 *+ C Ox-2in|x| +C + C 2+ 2x Ox-2injx + 21 + C + C (x + 2)2

A:

Q: +2t +3r dr

A: The given differential equation is: rt2+r2+2tdt+t2+3r2dr=0t2+3r2dr+rt2+r2+2tdt=0  Now comparing this…

Q: If X = U+v , y =U-V then Show that + 2 du? = 2) ( %3D nene Than ded uce that wok cu+ v*+ (u+v) g…

A:

Q: Using the substitution u = 2x – 1, prove that - -3 8 dx 1 (2x-1)3 25

A: The given integral is ∫13x(2x-1)3dx Put 2x-1=t⇒2dx=dt when x=1 then t=1 and when x=3 then t=5 So,…

Q: -dx. (3x² + 1)ª Evaluate -1 +C OA. 18(3x² + 1)³ O B, In(3x2 + 1)ª) +C 1 OC. + C 18(3x² + 1)³ x2 +C…

A: Given- ∫x3x2+14 To find- The value of the integral

Q: h zp dy +6. +9y= dx² dx r²e-², 2

A:

Q: d di V(I + t*)s

A: Given ddx1+t757

Q: Determine the antidifferentiation of (3xc + ed - (4/x)) dx  (where c; d are real numbers and c does…

A:

Q: e2" – e5r dr dx b)] Jx (1 + x) + e3r

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Q: 4x -1 b) dx. J x(x? + x – 6) c) xV4-x² dx.

A:

Q: What is the value of x in (2x - jy) + (y - jx) = 1 - j5?

A: We have to find the value of x where 2x-jy+y-jx=1-j5

Q: Find // VdA, + 1 R -dA, R= [0,3] × [−1,1]

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Q: Prove (A N (B U C) = Ā U (B U C) %3D

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Q: 7. (50 u) du + (3v - 7u) dv 0. ANS. (3v +u) = c(v u).

A:

Q: Re(ze²), where z = 2-3mi

A:

Q: If z = 1 - 2j and w= 2 - 3j, express 2. w in the form a + bj where a and b are real.

A: Given  z=1−2jw=2−3j

Q: Creani Cet G4)= ti t2+34)j +4k HICH) = 2JF L+3tj + find a) H4) XG4) (1+24)k こ b) G4). HGE)

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Q: Ob.2 amom +C Evaluate +Vrdx Oa.5 2 5 3 2 Oc 2 wn +C Od 3 +C 2/3

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Q: make use od auxiliary questions to solve (y²+yz+z²)dx + (z²+zx+x²)dy+(x²+xy+y²)dz=0

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Q: | (4z + 4y + 4+8zy) dA where R= [1,2] x (0,1]. R Let I Find

A: Given: ∬4x+4y+4+8xyddwhereR=1,2x0,11

Q: Paove that b the total ditfesential equation Po) de +Q d y + R)d2=0N Integaable it and only it dR-dp…

A:

Q: (42ª + 3y² + 2z)dV B = {(z, y, 2) | 0 < I < 10, 0 < y < 8,0 <z< 1} .

A: Let's find.