Mytiply x-J (xJB 2X i

Q: (Tlog3(cosh z) + csch x) tanh x dx

A: Here we have to integrate the given Integral

Q: 2dx J x (3(ln x)2 + 12 ln a – 15) -

A: Answer

Q: cosh z sinh dz (cosh z+3) 2.

A: To evaluate the given integral.

Q: 2dx J = (3(ln x)² + 12 In x – 15)i -

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Q: ential equati x²y dy = C

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Q: ation. 11. x + 2x + 5 = 0 14. 9r2 + 12r + 4 = 0

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Q: f(x) = -(x ² + x-30 (x, f(x) Axis of symmetry: ● X-int (smaller) x-int (Larger) Form: Standard •…

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Q: b) Evaluate: i) Sx(V ++x) dx -2 10 dx ii) J1 x(10+Inx)³ jii) Jo 1+x? dx

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Q: terentiation 2 2 Find dy if y=x'+ sinxy 1.

A: Since you have asked multiple questions, as per the guideline we will solve the first question for…

Q: = z² sin ydy = (x²e² Inr + ze²)dx

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Q: Use variation of parameters to find the general solution: x^2y''+xy'-y = ln (x)

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Q: 7. f(x) = sech"(vi-x) 8. y = sech Inx

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Q: 2) Integrate using trigonometric substitution (a) s dx 4- x² (b) S, dx Vx2- 9

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Q: (х + 3)2 dx. J V40 – 6x - x²

A: Evaluate ∫x+3240-6x-x2dx=?

Q: reduction formula to evaluate the integral. x e 4Xdx

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Q: Jo logsinx dx by Q3) Evaluate the integral trapezoidal method (use h-D)

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Q: x dx 5. J 3-x2-6x

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Q: x 3 X 14.J. J16-x 2 -dx V16-x² dx 15. Vx -1 4

A: Use integration rules

Q: eYdx+ costx dy co

A: We have the given equation as   e-ydx+cos2xdy=0   We have to solve this differential equation

Q: 25. х — 5 dx x.

A: Hello! Thank you for your question. We’ll answer the first question since the exact one wasn’t…

Q: improper iterat 1/x3 y dy dx

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Q: 2. S dx exte-x 3. fx sec² x dx 4. esinx cos x dx

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Q: b) Roots: 2 ± v5 Y-int: 3

A: Topic : quadratic equation

Q: QI Find dy for 2y2/3+xy3/20 x 0

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Q: Che number ofunits in Z31[x] is

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Q: 2+ X 50 -x + 4y dy dx 2-X

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Q: tergal / 1 dx using the residue theorem. (x2 + 1)3

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Q: ations x2 + v² – 2x – 2v

A: Transform from polar to rectangular: a)We know x=r cos θ, y=r sin θx2+y2=r2tan θ=yx

Q: J2-x² (X +2y) dy dX

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Q: S-dx = In|x| + C and Sdx = In|x2|+ C. %3D %3D

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Q: y 3D 1 y = secxtanx; y

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Q: II. Perform the integration. 2 1. csc- x cot xVcsc x – 1 dx 6

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Q: Solve using variation of parameters or reduction of order (D² + 1)y = sec*x

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Q: 1+iz : If w = Find the im age of z|<1. 1-iz

A: Let the transformation be f(z)=w, in which x-y plane is converted into u-v plane.  Where z=x+iy and…

Q: 'a-x - dx atx valuate

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Q: 5 dx J (x - 1)(x2 + 4)

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Q: Integrating Factor by Inspection: 7. xdx + ydd = (x² + y²)dx

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Q: x dx using Sim | size 0.3 is

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Q: f(x) = arctan (V2x + e-4z

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Q: x² 1 arctan 16 2(x – 3) + 3 -dx = J (2x² – 6x + 13)² + c 2 x² – 6x + 13

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Q: Use integrating factors to solve (x² + y² + x)dx + xydy = 0.

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Q: 5 cosh 2t +-sinh 2t 2 -2t 3. L{

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Q: Use integrating factors to solve (x² + y² + x)dx + xydy = 0. %3D

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Q: dx x(3vx+1)

A: Given integral is ∫dxx3x+1

Q: Hiw 2 4t é dt 2 O Sx Sečx dx

A: (1) Consider the given integral. I=∫csc3dx The reduction formula is defined as.…

Q: 2. Find b such that dx 1+x2 3

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Q: sinhçc+y)= sinhx.coshyFcoshx:sinhy

A: Here we have to prove that   sinh(x+y) = sinhx.coshy + coshx.sinhy    and   sinh(x-y) = sinhx.coshy…

Q: 2.x +1 dx. J 6x +x-15 (ii)

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Q: dx 4. S x²Vx2-9

A: 4). Given: I=∫dxx2x2-9   ....(1)   As we know from the trigonometric identities; 1). cosx=1secx 2).…

Percentage

A percentage is a number indicated as a fraction of 100. It is a dimensionless number often expressed using the symbol %.

Algebraic Expressions

In mathematics, an algebraic expression consists of constant(s), variable(s), and mathematical operators. It is made up of terms.

Numbers

Numbers are some measures used for counting. They can be compared one with another to know its position in the number line and determine which one is greater or lesser than the other.

Subtraction

Before we begin to understand the subtraction of algebraic expressions, we need to list out a few things that form the basis of algebra.

Addition

Before we begin to understand the addition of algebraic expressions, we need to list out a few things that form the basis of algebra.