All categories

3 years ago

Evaluate the integral. (use c for the constant of integration.) 8 sin2(x) cos3(x) dx

1 answer:

3 0

Important formula we will use.
First formula
2 cos α sin β = sin (α + β) - sin (α - β)
Second formula
∫ sin x dx = - cos x + c

We should change the trigonometry expression from multiplication into addition. Use the first formula above
∫ 8 sin (2x) cos (3x) dx
= ∫ 4 ( 2 sin (2x) cos (3x) dx)
= 4 ∫ 2 cos (3x) sin (2x) dx
= 4 ∫ sin (3x + 2x) - sin (3x - 2x) dx
= 4 ∫ sin 5x - sin x dx

After changing into addition, solve the integration. Use the second formula.
= 4 ∫ sin 5x - sin x dx
$= 4(- \frac{1}{5} cos5x-cosx)+c$
$= - \frac{4}{5} cos5x-4cosx+c$
This is the answer.

You might be interested in

Combine the like terms for the following equations:

ololo11 [35]

1) 15x-24

2) 3b^2

3) m^2-2m-5

4) 14p+7

Hope this helps

mark me as brainiest pls

5 0

3 years ago

Make the subject of the formular A=arh C=2Ar

prohojiy [21]

Answer:

Step-by-step explanation:

I think this is it but you question want super clear

A = C/2r

3 0

3 years ago

Grace is comparing cell phone plans. A prepaid phone plan costs $0.20 per minute and has no monthly fee. A contracted phone plan

Sophie [7]

Answer:

Step-by-step explanation:

The contracted phone plan will have the same steepness and a higher y-intercept.

4 0

3 years ago

Which situation is most likely to show a constant rate of change

Firdavs [7]

Answer:

B. The amount spent on grapes compared with the weight of the purchase.

Step-by-step explanation:

A: The shoe size of a young girl compared with her age in years. For the first few years of a girl's life, her shoe size is relatively the same. When she goes through a growth spurt, her shoe size increases exponentially. So, that is not a constant rate of change.

B: The amount spent on grapes compared with the weight of the purchase. In most grocery stores, grapes are sold based on their weight, like $2.50 per pound. With each increase in 1 pound, the cost increases by $2.50. That is a constant rate of change.

C: The number of people on a city bus compared with the time of day. This value widely changes throughout the day. For example, during rush hour, there will be many people. But during times at, say, 2 to 3 AM, there will not be many people. So, this is not a constant rate of change.

D: The number of slices in a pizza compared with the time it takes to deliver it. The number of slices in a pizza never changes, so it does not depend on the time it takes to deliver. There is no rate of change.

So, B is your answer.

Hope this helps!

3 0

3 years ago

Simplify completely and find the restrictions on the variable.

MatroZZZ [7]

Answer:

$\displaystyle \frac{x + 2}{x + 9}, \ x \neq -9, \ 12$

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Algebra I

Terms/Coefficients
Factoring

Algebra II

Discontinuities
Domain Restrictions

Step-by-step explanation:

Step 1: Define

$\displaystyle \frac{x^2 - 10x - 24}{x^2 - 3x - 108}$

Step 2: Simplify

[Fraction] Factor numerator: $\displaystyle \frac{(x - 12)(x + 2)}{x^2 - 3x - 108}$
[Fraction] Factor denominator: $\displaystyle \frac{(x - 12)(x + 2)}{(x - 12)(x + 9)}$
[Fraction] Divide: $\displaystyle \frac{x + 2}{x + 9}$

We know that x cannot equal -9 because we would get a divide by 0 (undefined) error. We also know that x cannot equal 12 because it was canceled out when simplifying.

7 0

3 years ago