### Finding Integrals Using the Fundamental Theorem of Calculus

Using the Fundamental Theorem of Calculus I need to find the solution of the following problems. Can you explain how? Please see the attached file for the fully formatted problems.

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Using the Fundamental Theorem of Calculus I need to find the solution of the following problems. Can you explain how? Please see the attached file for the fully formatted problems.

Consider the graph of f(x): a)Can you draw a graph of F(x), the antiderivative of f(x), where F(0) = 1. b) Draw a graph of f(x).

Need to find the antiderivatives. (See attached file for full problem description)

F(t) = 10,000 / 10 + 50e ^-0.5t HOW do I obtain the derivative? What is the "e" portion of the problem? I know the derivative = 250,000e^-0.5t/ (10+50e ^-0.5t)^2 Please describe in detail the steps taken to arrive at this answer. For example, Why is the top of the equation 250,000e^-0.5t? Why is the bottom (10+50e^-0

Consider the heat equation delta(u)/delta(t) = (delta^2)(u)/delta(x^2) Show that if u(c, t) = (t^alpha)psi(E) where E = x/sqrt(t) and alpha is a constant, then psi(E) satisfies the ordinary differential equation alpha(psi) = 1/2 E(psi) = psi, where ' = d/dE is independent of t only if alpha = - 1/2. Further, show th

Please see the attached file for the fully formatted problems.

A hospital parking lot charges $ 2.50 for the first hour or part thereof, and $1.25 for each additional hour part thereof. A weekly pass costs $50.00 and allows unlimited parking for 7 days. If each visit Johnny makes to the hospital lasts two and half hours, what is the minimum number of visits that would make it worthwhile to

This is a study guide for the final exam in Calc 3. Thanks. (See problem set in attached file)

--- The area of a regular polygon with n sides which is inscribed in a circle of a radius 1 is: (see attachment for equation) Find the limit as by substituting and writing the limit in terms of u, then evaluating that limit. Do you get the expected answer? Thank you! --- (Complete problem found in attache

Can you help solving the problem and show how to graph? --- Consider a parabola . How to find a, b, and c that satisfies the following: (see attachment). Graph the parabola. Thank you for your help! --- (Complete problem found in attached file)

I need help with this problem for work: F(s)= 1/((s+3)^2)

Use Laplace transforms solve the initial-value problem. y'' + 2ty' - 4y =1 y(0)=0, y'(0)=0

If f(t) is a period, continuous function with period T>0, show that its Laplace transformation is... (See attachment for full question)

I am looking for a detailed solution. I need set up, solving, and final result. Therefore, I need solution of the second order DFQ. Finally for the description of the movement as time goes to infinity, I need what type of motion is that. a. An 8lb weight is attached to a spring suspended from the ceiling. When the weight come

I need to know how to find a particular solutions to an initial conditions. i know how to find the explicit solution of a differential equation but cannot remember how to find particular solutions. please show your working to help me understand. thanks Problems (also attached): Given the attached information: 1) So how

Using Laplace transformations solve the Initial Value Prblem: y"-2y'+10y=1 y(0)=1 y'(0)=2 For the solution please use laplace transformations and partial fractions.

Solve the Initial Value Problem where g(t) is the function graphed and it is attached to this problem. Solve the following differential equation: y"-3y'+2y=g(t) y(0)=1 y'(0)=0

A) Solve the Initial value Problem: y"+y=dπ(t)+d2π(t)+d3π(t)+......dnπ(t) ******dπ.- meaning delta sub index phi******** b) Graph the solution on the interval [0,3π] c) Discuss the behaviour of the solution in relation to the equation. I am looking for a solution for this problem. I need the

I) Find in implicit form, the general solution of the differential equation: dy/dx = 12y^(4/3)sin x cos^5 x (y > 0) ii) Find the corresponding explicit form of this solution.

∫ (x^5)/[(1+x^3)^(3/2)] dx ∫ {square root of [(x+3)/(x+1)]}dx ∫ (cot^3 v)[(csc v)^(3/2)] dx (I will use the $ sign for the integral sign) Problem #1: $ (x^5)/[(1+x^3)^(3/2)] dx the power 3/2 in the denominator is throwing me off greatly, as is the greater power (x^5) in the numerator. attempt 1

Determine whether or not the given function is periodic. Find the fundamental period. (h) sinh x (q) cos(sin x) Please see the attached file for the fully formatted problems.

A seismograph is a scientific instrument that is used to detect earthquakes. A simple model of a seismograph is shown below. It consists of a particle of mass m to which a pointer is attached. The particle is suspended by a spring of natural length lo and stiffness k and a damper of damping constant r from a platform of height d

Let y1, y2 be twice differentiable functions on an interval (a,b) whose Wronskian is nowhere zero. Show that there... Please see attached.

I am looking for the best statements about solutions and how is the statement supported... Please see attached.

Find general solution of a second order differential equation.

Ref. M4. use graphical methods to find the differential coefficient of simple sinusoidal and exponential functions. Please help with correct steps and formulas to get answer. Please see attachment

I am in Freshmen Level Calculus. We are in section 4.5 of the Salas, Hille, and Etgen book, "Calculus: One and Several Variables" 9th edition. The name of the chapter is The Mean value theorem and its applications, But from my understanding of the examples, It does not use the MVT. The previous sections were about local ex

I am in Freshmen Level Calculus. We are in section 4.5 of the Salas, Hille, and Etgen book, "Calculus: One and Several Variables" 9th edition. The name of the chapter is The Mean value theorem and its applications, But from my understanding of the examples, It does not use the MVT. The previous sections were about local extre

Find the equation of the attached inverse function, if the function is invertible.

Find the vertex and intercepts for the quadratic function and sketch its graph y=x^2+4x