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Integrals

Find the definite integral

(See attached file for full problem description) Find the definite integral __ ∫-18 3√x dx Note - The 8 is supposed to be directly over the -1.

Evaluating Integrals

Find the value of the integral - 6 ∫ x dx 4 Note - The 6 is supposed to be directly over the 4.

Integrals

Antidifferentiation ∫(e^x -6) dx

Definite integral

Evaluate the definite integral, use a graphing utility to show your results: (see equation in attached file)

Finding the Volume of a Solid of Revolution

Problem: The region R is bounded by the graphs of x - 2y = 3 and x = y2. Find the integral that gives the volume of the solid obtained by rotating R around the line x = -1. I'm having a hard time setting up the integral, I think that I have the concept for finding the area of a 2d object using an integral but can't figure out

Finding Integrals (8 Problems)

(See attached file for full problem description with proper symbols) --- Answers and working for Integration questions: 1.Integrate the following functions with respect to . (i) sin(5 - 4) (ii) cos(3 - 2) 2. Integrate the following functions with respect to x. (i) 4e-3x (ii) (

Applications of Integrals : Velocity and Acceleration

Newton discovered that the falling acceleration of all objects in a vacuum, regardless of their sizes and weights, is the same. A raindrop falls down to earth with the same acceleration as a big metal ball drops from the edge of a building. He came up with the value of 9.8 meters per square second (s2) for the falling accelerati

Integration, limits, and curves

Note: x is used as a letter only not as a multiply sign 1. Find the volume of the solid generated by revolving the region enclosed by y= x^(1/2), y=0, x=4 about the line x=6. 2. Find the arc length of the graph of the function y = x^(3/2) - 1 over the interval [0,4] 3. Integrate ∫ [(Pi / 2) / 0] x cos x dx

Cartesian Coordinates, Convergence and Divergence

1. Find the equation of the tangent line in Cartesian coordinates of the curve given in polor coordinates by r = 3 - 2 cos Ø, at Ø= (π / 3) 2.Test for convergence or divergence, absolute or conditional. If the series converges and it is possible to find the sum, then do so. a) ∑[∞/n=1] (3/ 2^n)