8s2 + 12 8. F(s) = (s – 2)(s – 4)4

Q: 2 4 x + 8 d x (x+2) ³

A: This question is based on definite integral.

Q: Sexdx X(x²+2)

A:

Q: ii Sketch y = f(x), y= f¯'(x), and y = x _on the same set of axes.

A:

Q: 5. Use the substitution method to evaluate r1 5xe32+2 dr. 0.

A: To determine the value of the integral.

Q: Э3: 4ln(2x+3)%3D In 2+1

A: Given equation: 4ln2x+3=ln2+1 We know that the value of ln2=0.693147…

Q: (b): Evaluate: (8t³ – 9t² + 10)dt

A:

Q: (d) Е(2X- 4). (е) Е(6X+ 3)2 + Var(7X — 24).

A:

Q: (t+2)(t-2)=(t+4)(t-5)+6

A: Here we solve the equation for t.

Q: S L-₁ ((5 + 1)²) = eat + aebt (s Find a + b.

A: Inverse laplace transformation

Q: = 1+x T(₁) = 7(x) = 7 (x²) = 4 + 3x. 3-22 2.1 Find T( a +bx+en 2.2. 2 2 = d -x73x T(4-x + from the…

A:

Q: 8. Find the domain of f(r):

A: Given fx=x+3x−1

Q: ö even ppo o ppo o h(x)=-x5+3x?.

A:

Q: Q3:5how thout the +3x2k is Conservative?

A:

Q: L-1 (s+a)2+ω2. s+a

A:

Q: 68. (t + 4)(t + 4)(t - 4)(t - 4)

A: We will use here the property a2-b2=(a+b)(a-b)

Q: 3y-6(y+z)+y

A: Distribute -6.

Q: K K 10 7xー 12. 12- M 3x +6

A: that is 7x-10=3x+6 4x=16

Q: 7(z+2)=2(z+3)

A: 7(z+2)=2(z+3)7×z+7×2=2×z+2×3

Q: 15. 423-922 + 72 +3)e- dz

A:

Q: S3 ¹(s²-2s+2)(s²+2s+2)· e. L-11 7

A: In this question, we need to find the inverse Laplace of the given function.

Q: (8) lf (a-b-a) za 2b 29 (b-a-c) 2b = K²(a+b+c) ³ 2C (c-α-b) then K=

A: Given:a-b-c2a2a2bb-a-c2b2c2cc-a-b=ka+b+c3    .............1We need to find the value of k.

Q: (D3 – D)y = -2(1+x) + 4e* – 6e¬* + 96e3*

A:

Q: K = 5k² - √5. 5 + 1 5. - 1 5k - 1 = ?

A:

Q: s'-4S+5)². ±+ S 9 - 2.

A:

Q: e (t + 5t- 2)

A: Given, e2tt3+5t-2. The given function is can be written as, e2tt3+5e2tt-2e2t, By applying Laplace…

Q: Evaluate L{- (s2+ 64) (s – 6) |

A:

Q: (-4)* 5k +1 k=1

A: We have to find if the series convergent or divergent.

Q: (3): Evaluate 3e -5e +8 dx

A: To evaluate the given integral

Q: 3. (ey + 1)²e-dx + (ex + 1)³e¯*dy = 0

A:

Q: Z:5X++7X2 MaX 3メ1+2X2< +8mf) メ+X2< 12) ~ X2<4 (2) XナX2 70

A:

Q: 18y − 2(1 + 7y)

A: Simplify:

Q: The ſ(x² – 2)² dx is {A}x -x³ { B}x* – 4x² + C {c}x$ – 4x³ + 4x – {D}x – 4x + C + 4x + C

A: