48. f(x) = x² – 2, rs 0

Q: 1 Q2: Evaluate fo y² (x² + y²) dx dy

A: Given :∫01∫01-y2y2x2+y2dxdy

Q: 2 5+4y³ Evaluate f,* S* y dz dx dy

A:

Q: f (x+2) In (x+2) - 4 tc (x+2) Xt *+ 2

A:

Q: 9. If | f(x) dx = 20 and f(x) dx = 3.6, find f(x) dx.

A:

Q: 5) f(t)= 2te' 2 Ans. F(s) =- (s –1)

A:

Q: O ) -. x- -2 46. f(z) = 1/x. - -2 fe) = V3r + 1, x=0

A: Given: 44.  f(x)=x2,  x=−246.  f(x)=1x,  x=−248.  f(x)=3x+1,  x=0

Q: dy = ay + by", dt a > 0, 6 > 0, -∞ < Yo < ∞

A: A differential equation is given by, dydt=ay+by2 for a&gt;0, b&gt;0, y0&gt;0. The objective is to…

Q: 3+2s 17. F(s) %3D (s+4)(s²–3)

A:

Q: b) f(x) = e-2x – x In x + x – 7 e*-e-x c) f(x) : ex+e¬x

A:

Q: '5 ven f(x) dx = 19 and f(x) dx = 11, evaluate (a) f(x) dx. (b) F(x) dx. /5 (c) f(x) dx. '5 (d)…

A: Topic:- definite integration

Q: 14. Evaluate the integral: (x² + 3x)° dx A. (x* + 30)' + C 3 x* + 3x' + C C. +C (x² + 3x) + C В. D.

A:

Q: 21 11 | {(=) dz f(x) dx = where a = and b =|

A: Given: ∫821f(x)dx-∫811f(x)dx=∫abf(x)dx   We know that ∫acf(x)dx= ∫abf(x)dx+∫bcf(x)dx We can write by…

Q: determine L−1[F].

A:

Q: 14)* dy y = xv1 + x3 when x = 2 ; find dx O Option 2 1

A: We have to differentiate the given polynomial

Q: 2 4 Evaluate Sx dz dy dx 3

A:

Q: If S 3 f(x) dx = -9. 0. Then f f(In(x)) dx 2x 4 2 O None

A:

Q: 26. Evaluate (x³ + y² + z)dx dydz.

A:

Q: dey こてxニコッン alx

A: We have to find :- d2y/d2x= ?

Q: -2 (x² - y²)²] Evaluate: S₁ S² P₁² dx dy x+y

A: Let's evaluate given double integral.

Q: 18 12 f(x) dx – | f(x) dx = f(x) dx - where a = and b =

A: Find value of a and b.

Q: 6 1) Find the general antiderivative for f(x) = 1+ x?

A:

Q: 2 Find the general antiderivative of f(x) = 5x* + 4 + C

A:

Q: Q4. Evaluate : O (xy²) dx dy -√1-(x-1)²

A:

Q: 21 11 f(x) dæ f(x) dx f(x) dx - 8, where a = and b ...

A: The given integral equation is ∫821fxdx-∫811fxdx=∫abfxdx.

Q: (1)F (s)= s +9 2s2 +s -1 %3D

A: Given: L-1s+92s2+s-1

Q: 2. Suppose f(x) dæ -5 and f(x) dx = 6. Compute 2f(x)+ (3x – 4)² dx.

A: Answer is 41 Explanation is given below

Q: Use geometry to evaluate the following integrals.

A: Given: fx=2,0≤x≤53,5&lt;x≤10 we know that ∫010fxdx=∫052dx+∫5103dx…

Q: Q3: van fy = xy-1+ x.ln(x) J f(x,y) = x' + y* if it was

A: To find the partial derivative

Q: 11. Find two different antiderivatives of the function f(x) = 6x² +2ex. 1

A:

Q: 25 17 9. f(x)dz f(x)dr 7 f(x)dr J7 a where a = and 6 =

A: Given that, The equation is following, ∫725f(x) dx - ∫717f(x) dx = ∫abf(x) dx We have to find the…

Q: 4. If ( Inx dx = f(x)[In(x) + 1] + C, then f(1) = A 1 B D -1

A: Solution

Q: 2 O Finel F.S For Fex) = 2くxくだ 7. %3D 2. -2 37 2 2.

A: By Bartleby policy I have to solve first question, as these are all unrelated problems. These are…

Q: 2. Suppose that . f(x)dx = 9 and S g(x)dx = 4. Find the exact value of 2f(x)dx.

A:

Q: 2. Ex Fnd そ if Z=マ+S+v ノ イ=メS マニメe *S=yさ

A: Given function is, z=r3+s+v2 Where, r=xeys=yexv=x2y

Q: 10 F(s) s(s + 1)(s² + 8s + 15)

A: Given Fs=10ss+1s2+8s+15

Q: 2 If "IF(x)dx=6 and frox)dx=7.50mm [rodr then f(x) dx = 5

A:

Q: 9. If dy = xy² and if y = 1 when x = 0, then when y = 3, x is equal to dx 0 -0 DIE

A:

Q: 23 14 f(x)dx – ¹ f(x)dx - - where a = = b [ f( and b = f(x) dx

A:

Q: Q5. Evaluate ſ^₂ ¹¹ xy dx dy. ry+1 y²

A:

Q: 3t when LI 1 ニe then L %3D S- 3 S-3

A: If Laplace transform of the function f(t) is denoted by Lf(t) or F(s), then the Laplace inverse of…

Q: 9. f(t) = (5+ e4t+t') 10. y = In(1 – 5x² + x³) 11. y = ³) In (x2 + 4x

A: Since you have posted multiple questions. As per guidelines we will solve only first question  If…

Q: dy dz 2. x+1 y+1 z+1

A:

Q: - 3-z2-y 2. Evaluate L* L z dz dy dx -5+x²+y²

A:

Q: 1) If h(x) = x³ +1, find h-'(x). (A) h-'(x) = 3+ (x +2)³ (B) h-(x) = Vx – 1 (C) h-(x) = 2r³ – 3 (D)…

A:

Q: 5. fx² In x dx

A: See the details solution in below

Q: .5 If f(x)dx 4 and | f(x)dx =7, then f(x)dx = %3D

A: Answer is below

Q: 1. Solve (6re",x0 b. [3cos 2xsin 7.xdx

A: here we have to evaluate  a) ∫-11w(x)dx if w(x)=6x2ex3,x≤035x-3 , x&gt;0b) ∫3cos2x sin7x dx

Q: The integral X dx Vx2 – 4 3

A: To evaluate the given integral.∫12 xx2-43 dx

Q: 5. ydx - (x +3y')dy = 0 Ans. x = 6y In C

A:

Q: 5 If [F(x) dx f(x) dx = 7.4 and 1.°F(x) dx f(x) dx = 5.7, find [²1 f(x) dx.

A: