Hello have you wached slogoman

If anyone could help that would be great! The topic is calculus, and substitution + integrals. I need help with the ones circled

Alex_Xolod [135]

Answer:

$\displaystyle \int\limits^{\frac{-\pi}{2}}_{\frac{-2 \pi}{3}} {\frac{sin \ x}{1 + cos \ x}} \, dx = -ln(2)$

General Formulas and Concepts:

Calculus

Differentiation

Derivatives
Derivative Notation

Trig Derivatives

Integration

Integrals
Definite Integrals
Integration Constant C

Integration Rule [Fundamental Theorem of Calculus 1]: $\displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)$

Integration Property [Multiplied Constant]: $\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx$

Trig Integration

Logarithmic Integration

Step-by-step explanation:

Step 1: Define

Identify

$\displaystyle \int\limits^{\frac{-\pi}{2}}_{\frac{-2 \pi}{3}} {\frac{sin \ x}{1 + cos \ x}} \, dx$

Step 2: Integrate Pt. 1

Identify variables for u-substitution.

Set u: $\displaystyle u = 1 + cos(x)$
[u] Differentiate [Trig Derivative]: $\displaystyle du = -sin(x) \ dx$
[Bounds of Integration] Change: $\displaystyle [\frac{1}{2}, 1]$

Step 3: Integrate Pt. 2

[Integral] Rewrite [Integration Property - Multiplied Constant]: $\displaystyle \int\limits^{\frac{-\pi}{2}}_{\frac{-2 \pi}{3}} {\frac{sin \ x}{1 + cos \ x}} \, dx = -\int\limits^{\frac{-\pi}{2}}_{\frac{-2 \pi}{3}} {\frac{-sin \ x}{1 + cos \ x}} \, dx$
[Integral] U-Substitution: $\displaystyle \int\limits^{\frac{-\pi}{2}}_{\frac{-2 \pi}{3}} {\frac{sin \ x}{1 + cos \ x}} \, dx = -\int\limits^{1}_{\frac{1}{2}} {\frac{1}{u}} \, du$
[Integral] Logarithmic Integration: $\displaystyle \int\limits^{\frac{-\pi}{2}}_{\frac{-2 \pi}{3}} {\frac{sin \ x}{1 + cos \ x}} \, dx = -(ln|u|) \bigg| \limits^{1}_{\frac{1}{2}}$
Evaluate [Integration Rule - Fundamental Theorem of Calculus 1]: $\displaystyle \int\limits^{\frac{-\pi}{2}}_{\frac{-2 \pi}{3}} {\frac{sin \ x}{1 + cos \ x}} \, dx = -ln(2)$

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

Unit: Integration

Book: College Calculus 10e

8 0

3 years ago

What is 19 over 57 in simplest form

JulijaS [17]

19/57 in simplest form is 1/3 and is 0.333 in decimal form

5 0

3 years ago

All rational numbers are integers trure or false

slega [8]

True.

The rational numbers include all the integers, plus all fractions, or terminating decimals and repeating decimals. ... All natural numbers, whole numbers, and integers are rationals, but not all rational numbers are natural numbers, whole numbers, or integers.

3 0

3 years ago

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An article in Fire Technology, 2014 (50.3) studied the effectiveness of sprinklers in fire control by the number of sprinklers t

gregori [183]

Answer:

probability that all of the sprinklers will operate correctly in a fire: 0.0282

Step-by-step explanation:

In order to solve this question we will use Binomial probability distribution because:

In the question it is given that the sprinklers activate correctly or not independently.
The number of outcomes are two i.e. sprinklers activate correctly or not.

A binomial distribution is a probability of a success or failures outcomes in an repeated multiple or n times.

Number of outcomes of this distributions are two.

The formula is:

b(x; n, P) = $C_{n,x}*p^{x} * (1 - p)^{n-x}$

b = binomial probability also represented as P(X=x)

x =no of successes

P = probability of a success on a single trial

n = no of trials

$C_{n,x}$ is calculated as:

$C_{n,x}$ = n! / x!(n – x)!

= 10! / 10!(10-10)!

= 1

According to given question:

probability of success i.e. p = 0.7 i.e. probability of a sprinkler to activate correctly.

number of trials i.e. n = 10 as number of sprinklers are 10

To find: probability that all of the sprinklers will operate correctly in a fire

X = 10 because we have to find the probability that "all" of the sprinklers will operate correctly and there are 10 sprinklers so all 10 of them

So putting these into the formula:

P(X=x) = $C_{n,x}*p^{x} * (1 - p)^{n-x}$

= C₁₀,₁₀ * 0.7¹⁰ * (1-0.7)¹⁰⁻¹⁰

= 1 * 0.0282 * (0.3) ⁰

= 1 * 0.0282 * 1

P(X=x) = 0.0282

5 0

3 years ago

5/8 - 5/24 I am doing some homework my brain isnt working right now can someone help me out?

DIA [1.3K]

Answer:

5/12

Step-by-step explanation:

i just looked it up...

5 0

4 years ago

Read 2 more answers