.4 -1 sec J2 Evaluate x dx

Q: 3. Evaluate yn x dx

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Q: 1 2x Evaluate [(4x-7)ay dx.

A: To evaluate: ∫01 ∫x22x (4x−7)dydx Let I=∫01 ∫x22x (4x−7)dydx First evaluate with respect to y taking…

Q: t' sin(2t n(21*)dt Evaluate

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Q: X COS(x) dx = k 0. x)UIs x (b) – 1.1365 (c) – 1.3651 (d) -

A:

Q: 5. w = x tan-y - 2=

A: Given: w=xtan-1y-2xyz

Q: 2 (x-4) dx = (S %3D 2.

A: Given : The definite integral is ∫02 ( x - 4 )2 dx .

Q: f(x) = 7 exp[ cos (5x)] '(x) = ]

A:

Q: S For x 1/2 x-x3 dx and using the substitutionu=x1/2

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Q: 5) f(t) = f(t) = e¯2t/1+ sin2t

A:

Q: 17 (xr² + 3xy) dx - dy = 0

A: We can solve it by seperation method

Q: 2. Find each of the following derivatives: d 1 dx x° ,5 d x (י4x+ nא1 (3sin ,3 dx d (7) .3 dx d [tan…

A:

Q: 4. j(x) = x² sec x %3D

A: We can solve question no 4 as below.

Q: Non Homo (D4 − 1)y = 0

A: Differential equations

Q: 2.xy x² – y? Show that - = 0 if z= Tan

A:

Q: (a) (b) 1 / (1+1 (1 + tan²0)² de S² 1 x²√x²-9 dx

A: Here we can use substution for solving the questions.

Q: 1, -1 <x<O 3. f(x) = %3D 0Sx<1

A: Given function is fx=1     -1&lt;x&lt;0x       0&lt;x&lt;1

Q: Question 9 Evaluate: 3x* In(x) dx x + -x In x) + c

A:

Q: 6)x(t)=sin(t-3T)

A: Z- transform

Q: 4x dx. 12. Evaluate: J 3+x²+æ+1

A: the given integral is: ∫4xx3+x2+x+1dx we have to evaluate the given integral.

Q: B) Evaluate 3n 2 4 y sin(x) dydx 0 0

A:

Q: dx Select one: a. sec-(x2) + C b. 2 sec-(x) + C c. -sec-(x) + C d. 1 sec-1(x²) + C

A: We will use the substitution, x² = sec (theta)   Then we will proceed as follows :

Q: 5) (2xy -3y) dx + (x-x) dy = o

A:

Q: evaluate the integral.

A:

Q: S 1 C=S²x + Sin'x

A:

Q: 3. f (x) = e COSX – 2 0.1 = 4 Хи ||

A: See below

Q: 1 x+1 ST (2y-2)dydx Evaluate 0 °0

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Q: .2 Evaluate: xye dy dx 0 J1

A:

Q: 3 2 ²²(4-x²) dy dx = 7 0 true O False

A:

Q: xdy - cyt x2 cos (x)) dx = o

A: The solution is given below in the next step:

Q: Derive the reductive formula for S sec" (x) dx.

A:

Q: e) x + tan(xy) = 0

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Q: 2xydx+(x^2)dy=0

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Q: Q. 3. Evaluate the following 2 a) cos x dx . 2 b) [ dx . 4 x* +1

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Q: (D² – 4D + 3)y = 20 cos x

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Q: f(x) = (x² + + 6) cos(4x) 3 х

A:

Q: 4 dx L 11. 1 + (2x + 1)2

A: As per our guidelines we are supposed to answer one question, kindly repost the remaining question…

Q: 2 x²e¬2® dx. Compute

A:

Q: dx 1. Evaluate S- x Vx-

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: 2U y'sy tan(x) 2) yy's 2Xes

A:

Q: c. x dy = x exp(y-x*) dx ; when x-0,9=o %3D

A:

Q: dx Evaluate | x² + 2x +5 [(x+1)/] a. arctan +C arctan +C 4 [(x+1), |(x+1), с. arctan -C d. arctan +C

A: Let I is the value of given indefinite Integration.

Q: Evaluate: X + T/4 dx. -*/4 2- cos 2x

A:

Q: If f(x, y) = x² tan¯' (4) – y² tan¬1 (4) , then fy(0,0) = 1 -2 2 -1

A: Given: f(x,y)=x2tan-1yx-y2tan-1xy To evaluate: fxy(0,0) We know that fx(x,y) is partial derivative…

Q: 2. Find g'(x). -sin x g(x) = [? t²et dt %3D x3

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Q: 8. - Evaluate | 1 dx 1+x а. d. none of the choices b. 1/ 2 е. -co с. f.

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Q: 3 T - 2 Evaluate: J. Soves y cosx³dy dx

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Q: Evaluate: . dz dy dx x4+4 O T/24 O T148 O tan-(2)/24 O T/96

A: To evaluate ∫02∫0x3∫0y zx4 + 4 dz dy dx

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

A:

Q: 1. Find for the following functions : dx 3(x* - ' –1) 5) y (ans.:

A:

Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: