2) x (2t + 1)3/2, 0 s t s 1 X = A) B) 1 C) 3 D) 2

Q: Evaluate the line integral ſc 2y dx + 6x dy where C is the straight line path from (4, 1) to (6, 5).…

A: Given query is to find the integral.

Q: Show the only soution to ax = 1, a + 0, is x = a^-1|

A:

Q: Evaluate the line integral S 3ydx + 6xdy where C is the straight line path from (1, 2) to (6, 5). So…

A:

Q: find in Euler's way 2x ! y(0.1) de y(0)=1 , h=0.05 y' = y -- y

A: The general form for Euler's method is given by yn=yn-1+hfxn-1,yn-1.

Q: Theorem 8o4 ŏ In a parallileguam, oppesitiangles ale equal aie

A:

Q: 2. If mZMKL = 83°, mZJKL = 127°, and MZJKM = (9x - 10)°, find the value of x. %3D %3D %3D J MA

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

Q: 1 Using Convolution theorem, find (i) L (s+a)(s+b),

A:

Q: Given: mTRV = 60° M2TRS = (4x)° %3D Prove: x = 30 Z. 60° R (4x)° W

A:

Q: 2)Evaluate exdA ,Ris bounded by y = x² ,y = 1

A: By using Fubini's theorem we solve the given problem.

Q: y" = 5sin (2z) denkleminin çözümü aşağıdakilerden hangisidir? %3D

A:

Q: 2² + e4 z lim z 0 22 – e²

A: This is a form of infinity by infinity so we have to apply Lhospital rule that is differentiate both…

Q: DE : -t de dyx= 3et dt with indial conditins : xl0)=6 yl0)=1

A:

Q: 2), Compute SE. di where Fュく-,) C is s shown

A: The general form of a vector valued function in three dimensions is given by F→=F1,F2, where F1 and…

Q: Prove by mathematical induetion. Ine I+2 +2+2 +2° = 2.

A:

Q: 2) Eliminate the arbitrary enstant, 4 y= x*+ Cix + Cz e-X

A: Given problem:- Eliminate the arbitrary constants. of y= x² + C₁x + C₂ e-x

Q: af af дх ду af az and of. HINT [See Exam Find 24 fx, у, 2) : x² + y2 + z2 af af ду af az %3D

A:

Q: 2/3 Determine the length of x=| for 0<ys2. Assume that y is positive.

A:

Q: o what does it con s conditionally conv 1. onvergence for at is the radius of approximation of e √2,

A:

Q: In ARST (not shown), mZR 45° and mZS 64°. Find m ZT. %3D

A: Given that, In triangle RST, m∠R=45∘ and m∠S=64∘ To find:

Q: ove that 1 cosh(tanh) = -1 -1 < r < 1. V1- 2

A:

Q: et A be 4X4r nas non-brivial . -son-

A:

Q: Obtain the general soluti d²y 1. 7- y = 10sin²x

A: Given: d2ydx2-y=10 sin2(x)

Q: Compute (ax + by² + cz) dS over the sphere x +y +z² = 1.

A:

Q: Find and when (TU – V)² In(W – UV) = In(2) at the point (T, U, V, W) = (1, 1, 2, 4).

A:

Q: In Exercises 5–12, find and sketch the domain for each function

A:

Q: Region ¥=1=sino jn 1-st q4adrant enclosed by the eardieid

A:

Q: Compute 1. % 1+ vår + g2 dr, lal 2 1+ " 2. 1+ V2r-

A:

Q: Find the indico 6. 2. 3+ 2 1..2+4+8+ 27 t. 4. 3. 12, (4)"- n= %3D1 2.

A:

Q: 12) Show that D- ldi-dal between is shortest distance a x+ by + e2 of i ancd ax +by +Cz = dz?

A:

Q: If In(ax)dx = 2, then a = %3D 1

A:

Q: inlyralf Evaluste the +2) ě Snz.dz whre CiI21= 1, by any tw o methode and compone the resalt.

A:

Q: (x) = 3x +12x+2, %3D ues of a, b and c such that

A:

Q: 7 cos(z) Driented ris countercleckwise ortented rectangle with -2-i , 2-i, 2té, -2ti

A: Contour integration

Q: J sec° (10t) tan“ (10r) dt 4 10.

A:

Q: So So t² etu du dt

A: Given, ∫03∫0tt2etududt

Q: 火2sin C&) for ダチo fcx) = { for x =0 show that Con tinods or not

A:

Q: Q1 : prove 1 2(1–z) 3(1--z) dydxdz = 1

A:

Q: 2 dt 22. Evaluate o v9– 2t² 2 dy 3-y³ 24. Evaluate o v8-y'

A: 22)I=∫0129-2t2dtt=32 udt=32 duI=∫29-9u2 32duI=2 ∫11-u2 duI=2 sin-1uI=2 sin-12 t301I=2 sin-1(23)

Q: Prove that S. 8 dx √π 2

A: This question is related to integration using gamma function.

Q: Findd Fhie boundled by Ahe Cureo area 2. X= 3J-y' and x+Y=3 ーレ

A:

Q: pes of animals are treated by at least on r. Scott, and Dr. Baker)?

A:

Q: If [ In(ax)dx = 3, then a %3D 1

A:

Q: Find dr. J (1+z²)3/2 - In Vx² + 1 + x| + In |Vx² + 1 + x| - Ja? + 1 +c Vx² + 1 O Option 3 Option 1…

A: Let I= ∫x21+x232dx Let x=tanθ ⇒dx = sec2θdθ Substituting this in I, we get

Q: 10- Prove that a.b3D la+bl2- la-bl? /4

A: Prove that a.b= la+bl²- la-bl²/4

Q: l? sc tue suell metuozd to fired tue voune of te Solid genented the by rerolning the plene rgim…

A:

Q: 2. In AXYZ, PQ || XY . If XZ = 15, YZ = 12, and ZQ = 8, what is ZP? 2.

A: Use concept of similarity. In similar triangle, ratio of corresponding side are equal.