Mathematics, 25.03.2020 04:31 zarakanchi

Explain in words why each of the following integrals is improper. (a) integral from 2^(infinity) t^7 e^(-t^2) dt. (b) integral from (pi/4)^(pi/2) sec t dt. (c) integral from 1^3[dt]/[|t-2|] . (d) integral from 1^2 ln (t-1) dt.

Answers: 1

Show answers

Answers

Answer from: williamsvilletiles

1. Integral defined in an improper interval

$\int\limits^\infty_2 {t^7 e^{-t^2}} \, dt$

2. Integral of a function undefined at some point of the interval.

$\int\limits^{\pi/2}_ {\pi/4} {sec(t)}\, dt$

3. Integral of a function undefined at some point of the interval

$\int\limits^3_1 {\frac{dt}{|t-2|}}$

4. Integral of a function undefined at some point of the interval

$\int\limits_{1}^{2} {ln(t-1)} \, dt\\$

Step-by-step explanation:

Remember that there two types of undefined integrals.

1 - Integrals that are computer over an unbounded interval (in other words one of the limits is infinity )

2 - Integrals where the function is undefined at some point of the interval.

So, identify the first type the first type of improper integrals a kind of straightforward, but for the second type of improper integrals you need to understand the function you are integrating.

By "undefined" it is understood that the function has some kind of discontinuity, for example, the function

f(x) = 1/x

is discontinuous at 0.

Now lets see the examples given.

Sec(t) = 1/cos(t)

Rememebr that $cos(\pi/2) = 0$ , that's why the function the second integral is improper.

For the next function

$f(t) = \frac{1}{|t-2|}$

$f(2) = \frac{1}{|2-2|} = 1/0$

Thats a discontinuity as well, and 2 belongs to the interval of integration, that's why that integral would be improper.

And for the next one, remember that the ln(0) is not defined, therefore,

$f(t) = ln(t-1)\\f(1)=ln(1-1)=ln(0)$

and 1 , belongs to the interval of integration, that's why it would be an improper integral.

Answer from: Quest

1/5

step-by-step explanation:

the dice has 6 sides and there is only one 5 in a dice.

Answer from: Quest

i think it is everything has to equal 180 so, if i correct 4=c. 6=d. 8=a. 7=b. and the last question would be c. because they are parallel lines and they are congruent.

step-by-step explanation:

the reason everything has to equal to 180 is because that is how it works. i'm guessing that is its rule. 4 and 8 are congruent and parallel so, that would be 30+30 because they have the same number. it would equal 60. 6 and 7 are congruent and parallel so, that would be 30+30 because they have the same number. it would equal 60. 60+60 is 180. so, now you have your answer

Other questions on the subject: Mathematics

Mathematics, 21.06.2019 21:10, benallyadam2067

Hey free points ! people i have a few math questions on my profile consider looking at them i have to get done in 30 mins!

Answers: 1

continue

Mathematics, 21.06.2019 21:50, shay68596

What is the next step in the given proof? choose the most logical approach. a. statement: m 1 + m 2 + 2(m 3) = 180° reason: angle addition b. statement: m 1 + m 3 = m 2 + m 3 reason: transitive property of equality c. statement: m 1 = m 2 reason: subtraction property of equality d. statement: m 1 + m 2 = m 2 + m 3 reason: substitution property of equality e. statement: 2(m 1) = m 2 + m 3 reason: substitution property of equality

Answers: 3

continue

Mathematics, 21.06.2019 22:30, imran2k13

Factor the polynomial by its greatest common monomial factor.

Answers: 1

continue

Mathematics, 21.06.2019 23:30, vliu470

Acar loses a quarter of its value every year. it is originally worth $35,000. to the nearest dollar, how much will the car be worth in 8 years?

Answers: 1

continue

You know the right answer?

Explain in words why each of the following integrals is improper. (a) integral from 2^(infinity) t^7...