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Integrals

Solve Sequences Used in Given Situation

There is a rope that stretches from the top of Maidwell building to a tree on the racecourse, and the length of this rope is 1km. A worm begins to travel along the rope at the rate of 1cm each second in an attempt to get to the other end. then a strange thing happens... some malevolent deity intervenes to make life even hard

Evaluating integrals

Evaluate the following integrals: (1)The integral of (6sin[2x])/sin(x)dx=____+C (2)The integral of (7-x)(3+[x^2])dx=____+C (3)The integral from 3 to 7 of ([t^6]-[t^2])/(t^4)dt=____+C (4)The integral of (6sin[x])/(1-sin^2[x])dx=____+C

Definite and indefinite integrals

Thank you in advance for your help. Evaluate the following definite and indefinite integrals: (1)The integral of (2x)/([x^2]+1)dx (2)The integral of [(arctan(x))/([x^2]+1)]dx (3)The integral of sqrt([x^3]+[1x^5])dx (4)The integral of (2+x)/([x^2]+1)dx (5)The integral of (2x)/([x^4]+1)dx (6)The integral from 0 to 2 of (x

Evaluating Integrals via Substitution

Thank you in advance for your help. Evaluate the integrals by making the given substitution: (a)The integral of x(4+x^2)^3dx; (u=4+x^2) (b)The integral of ((sin sqrt[x])/sqrt[3x])dx; (u=sqrt[x]) (c)The integral of e^(3sin(t))cos(t)dt; (u=sin(t))

Indefinite integrals

Thank you in advance for your help. Find the general indefinite integrals: (a)The integral of x(1+2x^2)dx (b)The integral of ((x^2)+1+(2/x^2+1))dx

Integrals : Rate of Change Word Problem

Water flows from the bottom of a storage tank at a rate of r(t)=200-4t liters per minute, where 0 is less than or equal to t and t is less than or equal to 50. Find the amount of water that flows from the tank during the first 10 minutes.

Integrals

Consider the definite integral I 4 I = ∫ e^x dx 0 1. evaluate the integral I directly by use of a suitable anti-derivative. 2. evaluate the integral I by use of a suitable Riemann sum and formally limiting that sum 3. evaluate the integral I by use of the trapezoidal rule: a) I T,2 - for 2

Deriving an integration rule

Derive an integration rule for the domain [0,1] based on the quadrature points x1=0, x2=1/3 and x3=1, which is exact for polynomials of degree <= 2. Please see attached for full question.

Integral of a Contour

Calculate the following integrals: &#8747; from 0 to &#8734; x^¼/(x²+9) dx Please see attached for proper format.

Integral of Continuous Decreasing Function on a Closed Interval

Suppose f(x) is continuous and decreasing on the closed interval (4 is less than or equal to x is less than or equal to 11), that f(4)=6, f(11)=3, and that the integral as 4 goes to 11 of f(x)dx=27.01678. What is the integral as 3 goes to 6 of f^-1(x)dx?

Properties of Integrals : Verify an Inequality

Use the properties of integrals to verify the inequality without evaluating the integral: [the integral as 1 goes to 2 of (sqrt(5-x))dx] is greater than or equal to [the integral as 1 goes to 2 of (sqrt(x+1))dx].

Integrals : Riemann Sum with Diagrams

This question has me going around in circles. I can't make the Sigma symbol on the computer, so I used the word "Sigma" instead. For (c), n is above the Sigma symbol and i=1 is below it. (a)Find an approximation to the integral as 0 goes to 4 of (x^2-3x)dx using a Riemann sum with right endpoints and n=8. (b)Draw a diagram

Elementary Numerical Analysis

GAUSSIAN NUMERICAL INTEGRATION 1. Consider approximating integrals of the form... in which f(x) has several continuous derivatives on [0, 1] a. Find a formula... which is exact if f(x) is any linear polynomial. b. To find a formula... which is exact for all polynomial of degree &#8804; 3, set up a system of four e

Integrals; Sine; Cosine; Bounded Region etc.

Please assist me with the attached problems. Examples: 2. Find each integral 5. Integrate equations using tables 6. Derive the sine squared formula 42. Use substituion to integrate certain powers of sine and cosine 52. Find the area of the region bounded by the graphs etc. (see attachment)

Find Areas and Sketch Bounded Regions (Curve) (10 Problems)

2. Sketch a vertical or horizontal strip and find the area of the given regions bounded by specified curves: a), b), c) and d) {see attachment!} 3. Sketch the region bounded by and between the given curves and then find the area of each region: a), b), c), d), e) and f) {see attachment!}