💬 👋 We’re always here. Join our Discord to connect with other students 24/7, any time, night or day.Join Here!

Get the answer to your homework problem.

Try Numerade Free for 7 Days

Like

Report

(a) If $ g(x) = \frac{(\sin^2 x)}{x^2} $, use your calculator or computer to make a table of approximate values of $ \displaystyle \int_1^t g(x)\ dx $ for $ t = 2, 5, 10, 100, 1000 $, and $ 10,000 $. Does it appear that $ \displaystyle \int_1^\infty g(x)\ dx $ is convergent?(b) Use the Comparison Theorem with $ f(x) = \frac{1}{x^2} $ to show that $ \displaystyle \int_1^\infty g(x)\ dx $ is convergent.(c) Illustrate part (b) by graphing $ f $ and $ g $ on the same screen for $ 1 \le x \le 10 $. Use your graph to explain intuitively why $ \displaystyle \int_1^\infty g(x)\ dx $ is convergent.

a. $g(x)=\frac{\sin ^{2} x}{x^{2}}$b. $\int_{1}^{\infty} \frac{\sin ^{2} x}{x^{2}} d x$ is convergentc. convergent

Calculus 2 / BC

Chapter 7

Techniques of Integration

Section 8

Improper Integrals

Integration Techniques

Missouri State University

Oregon State University

University of Nottingham

Idaho State University

Lectures

01:11

In mathematics, integratio…

06:55

In grammar, determiners ar…

06:08

(a) If $g(x)=\left(\sin ^{…

03:50

(a) If $ g(x) = \frac{1}{(…

04:59

(a) If $g(x)=1 /(\sqrt{x}-…

02:54

Consider the functions $f(…

10:34

(a) Use your calculator to…

02:02

02:27

Use the Comparison Theorem…

01:45

03:44

03:42

Show that $0 \leq e^{-x^{2…

for a. The problem is use your calculated our computer to Michael. Table off approximate wallows off integral from one two t jl box T X t issue Go to two five and one hundred for saland and ten seven. Does it appear that and a girl off one to infinity Xerox as compartment by computation when he is ico toe too far Turn The handwriting was selling them and seldom Auntie Girl off jail. Blacks from one two t is equal to there a point full for seven hours. There a point five seven seven one there a point six two one three point six six eight three zero point six seven three year old on DH zero point six seven three four It appears that Auntie girl off gearbox from one to Infinity Axe as merchant, since we can see the value as worry where it's more, Alba is smaller than one B. It was a comparison theory, um, with a fax it coach one over X Square to show that this improper, integral as burdened a party me now integral off Jill Box one to infinity The box is he cultures integral from wanting unity. Sign X squared over. Explain, Jax, but we know Sign X Square as always, smaller than one. So this is smaller, integral from one to infinity. One over x Square E X But we know this improper integral is convergent. So by comparison, Miriam the improper integral of Jill Lax from Want Infinity It's convergent Potsie. Look at the graph here. The writer curve is the Kif of one over X Square. On it's a blue curve is jewel box. We can see Blue Cliff is always and, uh, by the one, and we know it's anti girl. From what? From one to infinity, it'sjust area Ondas a curve on DH X axis. So Auntie girl off the gearbox is small isa into your off a phone box and they use York graft to explain intuitively why the improper into girl off to blacks is convergent this way. Now Integra off Jill blacks from one to infinity is the area, and there's a cure. If a blue one Andi X axis we can see when she won axe is richer than spot six. Jim Wax as almost zero so we can guys area is find that it's not infinite

In mathematics, integration is one of the two main operations in calculus, w…

In grammar, determiners are a class of words that are used in front of nouns…

(a) If $g(x)=\left(\sin ^{2} x\right) / x^{2},$ use your calculator or compu…

(a) If $ g(x) = \frac{1}{(\sqrt{x} - 1)} $, use your calculator or computer …

(a) If $g(x)=1 /(\sqrt{x}-1),$ use your calculator or computer to make a tab…

Consider the functions $f(x)=1 / \sqrt{1+x^{2}}$ and $g(x)=$1$/ \sqrt{1+x^{4…

(a) Use your calculator to approximate $\int_{0}^{b} e^{-x^{2}} d x$ for $b=…

(a) Use your calculator to approximate $\int_{0}^{b} e^{-0.00001 x} d x$ for…

Use the Comparison Theorem to determine whether the integral is convergent o…

Show that $0 \leq e^{-x^{2}} \leq e^{-x}$ for $x \geq 1$ (Figure 10$) .$ Use…