1 "F(s) = a. s² – 2s+17 s-1 O b. F(s) s(s? – 2s+5) 1 OC. F(s) s² – 2s+5 s-1 O d. F(s) s(s? – 2s+ 17) II

Q: (12) Find the Value of b such that: [3x² dx = 27 (A) 6 (C) 9 (B) 3 (D) none of these 4

A: Step 1:To find the value of b such that ∫0b​3x2dx=27, we need to solve the definite integral: Step…

Q: Find T 1 = -1 wwwman x² dx + C

A:

Q: 2x2 + 2x+1 dx. x+1 Evaluate: e

A: Please see the answer below.

Q: d®y dx + 17 + 88 + 144y = 0 dx dx2

A: Differential equations

Q: S(3x + V-) dx (b) Evaluate : ) dx

A:

Q: dy If dæ 4x³ + 3x? + 6x and y = -3 when x 1, fınd y. |3D

A:

Q: [D³ 6D² + 11 D - 6) y = tanx -

A: Sol:- Original Differential Equation can be re-written as :- y''' -6y'' +11y' -6y=tanxThe general…

Q: 3 (5æ° + 2x") dx - 4 Find

A:

Q: Find ¹ (3x + 5y)dA where D = {(x, y) | x² + y² ≤ 16, x ≥ 0}

A:

Q: Q5:A/ Find In x dx XVIN? x + 1

A:

Q: x /[x² – 9[ + 7 dx

A: LetI=∫07xx2-9+7dxEliminate absolute valueI=∫07x-x2+9+7dxI=∫07x-x2+16dxPut…

Q: L(t cos 2t] s2+2 (s2 +4) 8-4 (s²+4)? s2-2 (s2+4) s2 -4 (s2+4)"

A:

Q: •5 | Vx2 – 9 dx 3

A: Integral formulae: ∫x2-a2=x2x2-a2-a22lnx+x2-a2+C Given integral is: I=∫35x2-9dx Comparing given…

Q: Evaluate : ((x + Vx² +1) dx.

A: To find ∫x+x2+1ndx

Q: Evaluate: | V12 – 2| +x dx

A: Explanation of the answer is as follows

Q: 2(14 – 2)² dx = (14 – x)² dx %3D

A: ∫ x1314-x2dx=∫ 196x13-28x43+x73dx=∫ 196x13dx-∫ 28x43dx+∫ x73dx=147x43-12x73+310x103Add a…

Q: x2 +3 dx x (x2+2x+1)

A: This is a question of indefinite integrals.  To solve this question we will apply the concept of…

Q: 3) [ dx (x²+3)7/2 =

A:

Q: 2 (3г — 1) V 32? — 2х +3 dx -

A:

Q: -3 12 dx /5x+1

A: Basic rules of integration are required.

Q: -√2/2 x² √1-x² Evaluate √²/2 dx. Show the details!

A:

Q: 8х — 2 dx х3 — х 17x2 + 7x – 3 dx (x – 1)? (2x + 1) -

A:

Q: Prov that d dx 2cos2x = -2sin 2x

A: Solution is given below:

Q: | (cscx + 3 e3* š + 6" – 7) d.æ -

A: Given: ∫(csc2x+3e3x+6x-7)dx

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.