Find f(t). ℒ−1 {(3s-1)/s2(s+1)3}

Q: Solve the initial-value problem for x as a function of t. da (t - 10t + 21) = 1, (t > 7, z(8) = 0)…

A:

Q: Find the particular solution for f(x) with the given initial conditions. f''(x) = 4x3 and f'(1) = 5…

A: Given,           f''x=4x3  and f'1=5  and f0=50

Q: Solve the differendialegimaition: (2x+e)dx + (xay co

A: Make some simplification and rearrange the given differential in exact form.

Q: Find G'(x) In(8) (4e 6t 1) dt G(x) х G'(x)

A: Given:

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A:

Q: If P0 is the initial population at t = 0 and k depends on the rate of growth, then the formula for…

A: Given, P0 is the initial population at t = 0 and k depends on the rate of growth Population usually…

Q: Find the function f(x)  described by the given initial value problem f"(x)=2sinx, f'(pi)=-5,…

A:

Q: 2 3x 2. Evaluate f x'e* using integration by parts.

A:

Q: x² + x - 1 dx J, x(x2 – 1) is convergent or divergent.

A: We have to solve the integral and check it is convergent or not

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A:

Q: Solve the initial-value problem for x as a function of t. dx (2t3 – 2t? + t – 1) 12, г (2) — 0

A: Given,

Q: Drove that 3 e dx converges to 9 3e

A: Explanation and solutions is given below.....

Q: Derive a formula for In x dx where a. nt-1 b. n=-1

A:

Q: Solve the initial-value problem for x as a function of t . dx (2t3 – 2t? + t – 1)- = 3, x(2) = 0 dt

A:

Q: x² = 10) Evaluate the integral S dx, x > 3

A:

Q: Solve the initial-value problem for æ as a function of t . de = 3, x(2) = 0 (2t° – 2t? + t – 1

A: First, we separate the variables.

Q: b) Suppose x # 2. Find dif dx In y = In (x - 2)² √x² +1

A:

Q: Solve the ODE by y Integration a. = 0

A:

Q: Solve the initial value problem to find f(x), given 2 =1+ 4x? when f(-1) = 4 dx

A: Satisfied condition of differential equation

Q: Find f(x) by solving the initial-value problem. f'(x) = 5ex − 8x; f(0) = 9 f(x) =

A:

Q: Solve for F(s) L[(1+ e2t)²] a. 1 2 1 s's-2's- 4 Ob. 1 2 s - 2 s's+2 1 + s's+2' s + 2 d. 1 + s's-2' s…

A:

Q: What is the antiderivative of 1 / (x - (1/k)x^2) with respect to x? k is a constant

A:

Q: Solve the initial value problems in Exercise for x as a functionof t.

A:

Q: Use integration by parts to prove the reduction formula: п-1 S (In x)"dx = x(ln x)" – n [ (Inx)"-! п

A: 2

Q: 1. e-st cosh t dt 2x +4 2. 2x2 + 21x + 34

A:

Q: Q2: - If y = 3sec3t and x = etan3t prove that: - dy (In3)² dx y logy x * * -

A:

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A:

Q: Q2/Find the value of the integral dx 1+x² by using simpson method (n = 6)? 3

A: Find out the value of the integral using the simpson 1/3 method.

Q: Solve the initial-value problem for a as a function of t. dr 9, x(2) = 0 (2t* – 212 +t – 1) dt

A: We have to solve the initial value problem

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A:

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Q: The number N(t) of supermarkets throughout the country that are using a computerized checkout system…

A: The number N(t) of supermarkets throughout the country that are using a computerized checkout system…

Q: Evaluate the integral. 3x-7 (a) S- dx x2-2x-8

A: Answer and explanation is given below..

Q: Solve the initial-value problem for x as a function of t . dx (2t3 – 2t? + t – 1) - 3, г (2) — 0 dt

A:

Q: Q18: Evaluate the definite integral: 4x dx V1 + 2x²

A: To find the definite Integral  Substitute 1+2x^2 = t and change the limit accordingly

Q: Solve the initial-value problem for a as a function of t . dz (t² – 11t + 30)- 1, (t > 6, ¤(7) = 0)…

A:

Q: a'(t) = -x(t – 1), x(t) = 1 on [-1,0], is given by 1(t) = E(-1)* t – (k – 1))* k! for n-1<t <n, k=0

A: As per the question we are given the following first order time varient differential equation :…

Q: Solve the initial value problems for x as a functionof t. (t2 + 2t) dx/dt = 2x + 2 (t, x &gt; 0),…

A: t2+2tdxdt=2x+2⇒dx2x+2=dtt2+2t Now integrating on both sides, we get…

Q: c) Converge by integral test Q.10) fxe-x dx = a) 6e-5-1 25 b) 1-6e-5 25 c)(4+1) 2$ -6e-s 25 d)-

A:

Q: Solve the initial-value problem for x as a function of t . (2t³ − 2t² + t − 1) 12, x(2) = 0 dx dt =

A:

Q: se N.P.M. to estimate the root of -X = e -X for an initial of Xo =0

A: Here f(x)=e-x-x,  x0=0. We estimate the root of f(x)=0 by using N.R.M.

Q: Solve the initial-value problem for x as a function of t. (2t³ − 2t² + t − 1) = 0 dx dt = 3, x(2) =

A:

Q: Q1. Evaluate the integral S dx (x + 1)(x² + 1)

A: We need to evaluate the following integral ∫01dxx+1x2+1

Q: Find the net change in ve]locity over [1, 4] of an object with a(t) = 8t − t2 m/s2.

A:

Q: Solve the initial-value problem for a as a function of t. da 9, x(2) = 0 (2t – 212 +t – 1) – dt

A: We have to solve the initial value problem for x as a function of t.…

Q: Solve the initial-value problem for yy as a function of xx. (64−x2)dydx=1,y(0)=5(64-x2)dydx=1,y(0)=5

A: (64-x2)dydx=1⇒dy=dx64-x2integrating,                ∫dy=∫dx64-x2+c      [c=…

Q: Find the initial value of f(t), if: 2(s + 2) s(s + 1)(s + 3) F(s) = -

A:

Q: Compute f'(1) where f(x)=1/2 e-2x + ln(x2 + 1)

A:

Q: Q1: Use Newton - Raphson method to estimate the 3 Yoot of fcx) = x-X-1, employing an initial guess…

A: We have to use Newton-Raphson method which is widely used in finding the root of nonlinear…

Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.