-4 –x² x e?y dy dx= 4-у O 1 (e12 – 1) O 1 금(62-1) 2 O 1 8–1) O 1 (e8-1) 4 (e 12-1) (e?-1)

Q: d -(3x² + 11)e¬ª at x = –1. dx Evaluate

A:

Q: dx= A B e-1 © 1-)

A: I am going to solve the given problem by using some simple calculus to get the required result.

Q: 3. f; 3x – 1 -dx J 25х? -16

A:

Q: S(x + 1)(2 – x)° dx 7(2 - x)* - (2 - x)* +c 7(2 - x)* -(2 – x)* +c 3. (2 - x)* +(2 – x)* +c 금(2-x)*…

A:

Q: √ (9+x²) ²0 dx is equal to 3x a. + Arctan) + C 3x b. (+ Arctan) + C - 54 c. + Arctan) + C 27 d. - (+…

A:

Q: 1 + e1x+10 + 4" +x – 5) dx + xA 4x-

A:

Q: Determine d2y dx2 , if 2x3 − 3y2 + 7xy = 0

A: We can make it easier for you

Q: 1. у%3D х3 — 2x2 + 3х — 5 y = 3 — 2х2 + 3х — 5 dy — Зx2 — 4х + 3 dx

A: Given: y=x3-2x2+3x-5

Q: x*+2x-17 x4-16

A:

Q: C4

A: Given, Evaluate ∫ex1+e2xdx

Q: 1. Find 2(3z + 4)² dz.

A:

Q: If (In x)2 c (a (In x)? + b in x +c) + constant, then 2 a + 28 b + 18 c = 32

A: Solving the above given integral

Q: - In(1) none of the choices -5 - In(3) - In(4)

A: Integration of Rational Function: A function of the form , whereand are polynomials, is called a…

Q: xx5+G dx 4.

A: To find the integral , using a suitable substitution

Q: zV1 - (a – 1)}'da = a;+ :) a+b? What is

A: Given,             ∫12x1-x-12dx=a1b+πcTo find : What is a+bc.

Q: の 2dx (3×+12メ-15) ー2

A: Given I=∫23x2+12x-1512dx

Q: (a) S 5x2/3 +x5/3 + 3x+/3 dx (b) Sx² - 4 dx (c) Sa? — х — 2) (3- 4х — 2х?) dx

A:

Q: Find d da [e³²2²] dx 6xe ³x² e ³x² 6x e ³x² 6x (eª) (e³²²) (3x²) (6x)

A:

Q: 【g火) ニ

A:

Q: 2х + 1 бх2 + 23х — 9 dx х3 + 2х2 — 3х Ja- 2)(x – 3)² dx

A:

Q: I(x²-x)dx= O a. -30 O b. 5 O c. 9 O d. 0

A: Given integral is  ∫-22x3-xdx

Q: (x4 4x2 + 6) dx = 2 (x*-4x2 + 6) dx Select one: True False

A: Property of definite integral ∫-pp f(x)dx = 2∫0p f(x) dx , if f(-x) = f(x) or it’s an even function…

Q: -x-1)dx= -e-2 А. 2e е-2 В. C e+2 2e Зе- 2 D. 2e 2e

A:

Q: 1 e2x + 5ех 4 e2x + 4ex

A: Given: ∫ 14e2x+5exe2x+4ex dx= 14∫ ex+20ex+4 dx    (Multiply and divided by e-x)

Q: 6х —9 4.) dx 22— 3х +2

A:

Q: Find (2a° + 3x*) dæ + C

A: We evaluate given integral

Q: x²dx a. V2x-x2 x2 dx b. 1-х6

A:

Q: e2x 9) S dx 25-e4x

A: To find the value of the given integral, first we use substitute e2x=t, then we use the integration…

Q: 2х + у dy 3+ 3у? — х dx 3.

A:

Q: dx -(r+

A: We have to evaluate the following integral: ∫dx4-x+22

Q: S 1 (x + ²)² + ( √ 39 ) ² 2 dx

A:

Q: +1 dx -8 Evaluate

A:

Q: What is fxe- dx ? -x Oxe xee+C Ox²e-2x 2 + C X -xe-* — e * +C x² e-x 2 + C

A: Consider,

Q: 2.2 (x²-y² + sxy + 2) y.dx + ( x + ² + 4xy + 2)x.dy=0

A:

Q: (1 + x)" > 1 + nx

A:

Q: ay 3y fobit 2

A:

Q: A ezbx? dx 2

A: As per our guidelines we are supposed to solve only one question. For the solution of the first…

Q: Evaluate: xe² dx Ső 0e-2 0e² 1 - 0/(e-1) 22

A: Evaluate the integral

Q: 3 5). | e2x dx -1

A:

Q: y" – 10y + 25y = e5x

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: