Mathematics, 16.06.2021 05:00 1tallison1

\int\limits^0_∞ cos{x} \, dx

Answers: 1

Show answers

Answers

Answer from: rosaa7

$\displaystyle \int\limits^0_\infty {cos(x)} \, dx = sin(\infty)$

General Formulas and Concepts:

Pre-Calculus

Unit CircleTrig Graphs

Calculus

LimitsLimit Rule [Variable Direct Substitution]: $\displaystyle \lim_{x \to c} x = c$ IntegralsIntegration Rule [Fundamental Theorem of Calculus 1]: $\displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)$ Trig IntegrationImproper Integrals

Step-by-step explanation:

Step 1: Define

Identify

$\displaystyle \int\limits^0_\infty {cos(x)} \, dx$

Step 2: Integrate

[Improper Integral] Rewrite: $\displaystyle \lim_{a \to \infty} \int\limits^0_a {cos(x)} \, dx$ [Integral] Trig Integration: $\displaystyle \lim_{a \to \infty} sin(x) \bigg| \limits^0_a$ [Integral] Evaluate [Integration Rule - FTC 1]: $\displaystyle \lim_{a \to \infty} sin(0) - sin(a)$ Evaluate trig: $\displaystyle \lim_{a \to \infty} -sin(a)$ Evaluate limit [Limit Rule - Variable Direct Substitution]: $\displaystyle -sin(\infty)$

Since we are dealing with infinity of functions, we can do a numerous amount of things:

Since -sin(x) is a shift from the parent graph sin(x), we can say that -sin(∞) = sin(∞) since sin(x) is an oscillating graph. The values of -sin(x) already have values in sin(x).

Since sin(x) is an oscillating graph, we can also say that the integral actually equates to undefined, since it will never reach 1 certain value.

∴ $\displaystyle \int\limits^0_\infty {cos(x)} \, dx = sin(\infty) \ or \ \text{unde}\text{fined}$

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Improper Integrals

Book: College Calculus 10e

Answer from: Quest

step-by-step explanation:

i have done this all on a piece of paper but idk how to put it on here cuz it needs to be drawn

Answer from: Quest

The coordinates of point a right now is (-3,-1) you have to multiply these coordinates by a factor of 2 to get (-6,-2)
If abcd is dilated by a factor of 2, the coordinate a would be:

If abcd is dilated by a factor of 2, the coordinate a would be:

Another question on Mathematics

Mathematics, 21.06.2019 15:30

With: label the vertices and all the elements needed. find x

Answers: 2

Answer

Mathematics, 21.06.2019 19:00

Me with geometry ! in this figure, bc is a perpendicular bisects of kj. dm is the angle bisects of bdj. what is the measure of bdm? •60° •90° •30° •45°

Answers: 2

Answer

Mathematics, 21.06.2019 21:50

Which of the following equations is equivalent to x/3-6/x=1

Answers: 3

Answer

Mathematics, 22.06.2019 02:00

Use long division to indentify (12xto the second power+15x-8)divided by 3x

Answers: 2

Answer

You know the right answer?

\int\limits^0_∞ cos{x} \, dx...