3t L[e* (6 cosh(3€) – sinh(5t) ) O A. 6. (s – 3)* – 9 (s – 3)- 25 OB. S-3 (s – 3) (s- 3) - 25 OC. S-3 6. 1 (s - 3) -3 (s – 3) - 5 (s – 3)* – 5 OD. 6. (s – 3) -9 (s-3)- 25 S-3 OE. S+3 6. (s + 3) -9 (s +3)- 25 |

Q: dx 5 — 2х

A:

Q: 4 – 5x2 dx. ¤/3x² – 1 9. Evaluate -

A: To find the given integration.

Q: 3 4 dx . (5+2x)' 3. Evaluate

A:

Q: Find a number a + 5 such that S" (1 – æ) dæ = 0

A:

Q: Evaluale the to 312 bwiny dx 12

A:

Q: Evaluate O a. 3/4ln4 O b. 3/2ln2 O c. 2/3ln3 O d. 5/6ln6

A:

Q: 2.1 Evaluate f xvx +5dx (10 marks)

A: Given that   xx+5 dx Substitute u=x+5 →dudx=1  and x=u-5 ∫xx+5 dx=∫u-5 u du…

Q: 8. dx (36-262

A: Integrate by using trigonometric substitution

Q: Evaluate -o (i +1) 3° ui = 0

A:

Q: 2-8x Evaluate dx. 49-4x

A:

Q: 3 13 (3.) [ 1 5 dx 2 x 1 - 16x

A:

Q: 1 dx O (1+ x)1/4 1.

A:

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.