You found that the reduction formula of a certain integral is In = x"+2e2= - (n + 2) In-1 and that 1 e2a What is I, ? 2 1 1 2 2 1 1 1 4

Q: Find the indefinite integral.

A: Given: I=∫5t+63dt  ……1

Q: Evaluate the integral. In 2 e2X dx (Hint: eln a = a)

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Q: The value of the integral is equal to: Select one: O 4 O с صرا من م من ته 3 x ²² (4x - 4y) dy dx

A: The given integral is: I=∫01∫0x4x-4ydydx   As we know the Power rule: ∫xndx=xn+1n+1+C

Q: calculate the integral of: e(x^2/2)

A: We'll use the Maclaurin series expansion for e^(x^2/2).

Q: 2. Find the following indefinite integrals. 1 dx (a) 16 – [In(x)]² 1 xp (b) | x?+ 2x + 26 / A 1 (c)…

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Q: tan (In 4x) cos (In |(2x)"|)|+C. what is b? The integral of dx is b In A B 2 4 4

A: Given :  ∫tan(ln|4x2|)xdx=bln(|cos(ln|(2x)a|)| +C   To find : Value of b

Q: 2. Use integration by parts to prove the following reduction formula for integrals, where n is a…

A: Using definition of laplace transformation.

Q: The particular Integral for (D² + 19²)y = sin19z is Yp 38 O Yp 19 O None O Yp Zacon19z 38

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Q: (b) 'elz)x d: 1

A:

Q: Evaluate by algebra dx 1. S 3 1+ √x+1

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Q: Evaluate the integral. In 2 2 e sinh 0 d0 - In 10

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Q: Find the following indefinite integral. (5 -0.25x Jox=D -0.25x +3e d%xD (Type an exact answer in…

A:

Q: 2ェ dr Vェ? +1

A: We have to find the given integral.

Q: 2. Identify which of the following integrals are improper: 1 1 dx 1 fin(x)dx 1 X +3 1 fe* dr -dp- 3

A:

Q: a In x dx for the integral to be equal to 2 What should a be in O e? 0. 1 o 1 Ое

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Q: 1 Determine the definite integral of 4 3(Vx) xp (DE + x^)S

A: Let I=∫49x+13xdxApply the Sum Rule:…

Q: Q1/ Use Gauss-Legendre formula to evaluate the integral o e-dx withn= 3.

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Find the answer to this integral:

A:

Q: What is the integral of e^(3.4*x) from x=1 to x=6?

A: Solve the definite integration and put the limit.

Q: what is the integral of e^(-2a|t|) from 0 to w

A: Given integral: ∫0we-2atdt

Q: Evaluate the integrals in ∫8 e(x+1) dx

A: ∫8ex+1 dx Put  x+1=t⇒1+0=dtdx⇒dx=dt

Q: 2. Evaluate the given definite integral, if it exist. V4 + 3x dx

A: To evaluate

Q: 6. Evaluate the fallowing real integrals by residue theerem ? dX ニ ans : こ。(X+a?)2 493 • I- ans B 12…

A: Let's find.

Q: 3. Prove properties (3) and (4) analytically, by making x = -t in the part of the Integral from -a…

A: Concept:

Q: How do I find K of the integral e^(x^2/2)dx on the bounds from 0-2 what is E_T? and what must n…

A: Given: The error in trapezoidal rule is given as:

Q: 1 2x dæ is an improper integral. 1

A: The definite integral is called a proper integral if the interval [a, b] is finite or bounded and…

Q: by taking |In x · dx: solution of the integral with Simpson's 1/3 method Inx n = 2 which one? 1

A:

Q: Which of these is a non-elementary integral?" ( In(2y² + 1) -dy 4y A. * cosh(2x) xp. B. +…

A: (a) For, Is non elementary since y is in denominator. (b) For Is non elementary since x is in…

Q: 1- Find the integral of: A 2 cot - de 3 T7/2 А-

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Q: 5 Find the following indefinite integrals. 10 b. J- S(x+2)' dx a. (3x-7) xp-

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Q: 11. The integral of an(In|4x=12 dx is bln|sec(ln(2x)ª)|. What is b? A. 2 В. С. 4 D. I

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Q: The integral of sin2 3xdx is x 1 -x +A + C, What is the value of A if x =-. 4 O -1/12 O 1/12 O 1/18…

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Q: find the indefinite integrals. 1. ∫ e−0.05t dt 2. ∫ (3/t  -  2/t^2)  dt

A: case 1:The given indefinite  integral  is ∫e-0.05t dt.Let u = - 0.05t, then du/dt = -0.05.

Q: The value of the improper integral, if exists: S. 12 x e-a dx 1

A:

Q: d) Determine the infinite integrals of the following e+2 i. ii. 2 3 sin2x dx

A: Evaluation of the integral

Q: Evaluate the integral. In 5 2x 3 e X dx 0.

A: Basic integrals : →∫mneaxdx  = eaxamn Properties of Logarithm : →aln(x) = ln(x)a. →elnx=x.

Q: 2. Evaluate the following integrals. et a. (e2 +3)Ve2 – 16e-2" + 6

A: Solution

Q: ∞ Soo 8 2 "dx -7X e

A:

Q: Evaluate the integral analytically. 1 е бх 1+ e 6x

A: consider I= ∫01e6x1=e6xdx

Q: You found that the reduction formula of a certain integral is In = a" sin 2x + nx"-1 cos 2x – n (n –…

A:

Q: If g(1)=−5, g(5)=9, and ∫from 1 to 5 g(x)dx=−8, evaluate the integral ∫from 1 to 5 xg′(x)dx.

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Q: Q2:Solve the integrals as in below: 2-3y a² +b2 dy 1- j 2- S 3 (7* (7-3y 2)2 dy 0.5 2y 3- S -1 7 + e…

A: (Solving first three subparts as per our guidelines) Solution: 1.∫01yy5+1dy Now, ∫yy5+1dy…

Q: Q1 - Find the reduction formula for each of the following integrals iii. In = S x" cosh2x dx

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Q: d) Prove the results of the integrals 3 dx = 2+ In (2)– 4 [In (5)– In (3)]. x² +3x +2

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Q: Obtain a "reduction" formula that expresses the integral cos" x dx in terms of an integral of a…

A: Integration by parts: If u is first function and v is second function then: ∫u(x) v(x) dx=u(x)∫v(x)…

Q: THIS BE SOLVED ANALYTICALLY? SO, HOW? (a=0.75 STILL) dy=ay (1-2y). 6y³ - dt 4y³+5 SET UP THE…

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Q: 3. Find following integrals using method of substitution: Sze z dz a. 2 x2 b. S /1+x

A: Consider the provided integral, ∫ze-z22dz Find the expression for this integral using substitution.…

Unitary Method

The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products. 

Speed, Time, and Distance

Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.

Profit and Loss

The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.

Units and Measurements

Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.