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6 You want to approximate the integral $ x2 - x dx using T4. To do...
2. (5 pts) Use integration by parts to show that 1- x2 Write x2-x2-1+1 in the second integral and deduce the formula Now, use a trigonometric substitution to conclude that Evaluate 1- x2 dx by using the FTC and then verify your answer by interpreting the integral as the area of a familar shape.
2. (5 pts) Use integration by parts to show that 1- x2 Write x2-x2-1+1 in the second integral and deduce the formula Now, use a trigonometric...
I want to know when to use
shell method and when to use washer method. and how to evaluate the
improper integral.
1. Consider the region bounded by the graphs of f(x)-21 and g(x) 3-x2. 1.(a). (5 points) Write the integral for the volume of the solid of revolution obtained by rotating this region about the x-axis. Do not evaluate the integral. 24a). (I point) Is the integral dx an improper integral? 2.a). (1 point) Is the integral dx an...
Given the integral below, do the following. 2 cos(x2) dx Exercise (a) Find the approximations T4 and M4 for the given interval. Step 1 The Midpoint Rule says that b f(x) dx = Mn Ax[f(+1) + f(22) + ... + f(n)] with ax = . b - a + n a 1 We need to estimate 6 2 cos(x2) dx with n = 4 subintervals. For this, 1 - 0 Ax = 4 = 1/4 1/4 Step 2 Let žų...
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(1 point) Consider the following convergent series: Suppose that you want to approximate the value of this series by computing a partial sum, then bounding the error using the integral remainder estimate. In order to bound the value of the series between two numbers which are no more than 10 apart, what is the fewest number of terms of the series you would need? Fewest number of terms is 585 (1 point) Consider the following series: le(n Use...
Matlab code:
Task 5 As an engineer you are asked to calculate the approximate surface area of a lake in your local community. In order to do that, you decide to use a GPS to measure the x and y coordinates at various points around the lake. You pick a starting point and calibrate your GPS position at that point to be (0,0). You begin to walk around the lake collecting the following data below and eventually return to your...
Q1 2016
a) We want to develop a method for calculating the function f(x)
= sin(t)/t
dt
for small or moderately small values of x. this is a special
function called the sine integral, and it is related to another
special function called the exponential integral. it rises in
diffraction problems.
Derive a Taylor-series expression for f(x), and give an upper
bound for the error when the series is terminated after the n-th
order term. sint = see image
b)we...
how do I answer part (c)?
I. Consider the finite region bounded by the functions y-x and y x ) We want to compute the area of this region by slicing it in two different ways: using horizontal strips and using vertical strips. For each slicing direction, draw a representative slice and write a definite integral that gives the area of the region. Vertical strips Aorizontal strips 15 05 05 05 05 1.0 1.5 05 15 05 -05 Integral: Integral...
008 Notes points The table gives the values of a function obtained from an experiment. Use them to estimate f(x) dx using three equal subintervals with right endpoints, left endpoints, and midpoints. 5 67 8 9 (a) Estimatef(x) dx using three eqa subintervals with right endpoints. If the function is known to be an increasing function, can you say whether your estimate is less than or greater than the exact value of the integral? less than e greater than o...
All of 10 questions, please.
1. Find and classify all the critical points of the function. f(x,y) - x2(y - 2) - y2 » 2. Evaluate the integral. 3. Determine the volume of the solid that is inside the cylinder x2 + y2- 16 below z-2x2 + 2y2 and above the xy - plane. 4. Determine the surface area of the portion of 2x + 3y + 6z - 9 that is in the 1st octant. » 5. Evaluate JSxz...
How to do part (c) and part(d)?
How to do part (c) and part(d)?
(a) Evaluate the integral 2 48 dx Your answer should be in the form kr, where k is an integer. What is the value of k? darctan(x dx r2+1 (b) Now, lets evaluate the same integral using power series. First, find the power series for the function f(x)-Then, integrate it from o to 2, and call it S. S should be an infinite series. What are...