. The sum of two consecative integers is three times of their difference. what is the

If anyone knows about definite integrals for calculus then please I request help! I

kicyunya [14]

Answer:

$\displaystyle \int\limits^9_5 {\frac{1}{x^3}e^\big{4x^{-2}}} \, dx = \frac{1}{8} \bigg( e^\Big{\frac{4}{25}} - e^\Big{\frac{4}{81}} \bigg)$

General Formulas and Concepts:

Calculus

Differentiation

Derivatives
Derivative Notation

Derivative Property [Multiplied Constant]: $\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)$

Basic Power Rule:

f(x) = cxⁿ
f’(x) = c·nxⁿ⁻¹

Integration

Integrals

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

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

U-Substitution

Step-by-step explanation:

Step 1: Define

Identify

$\displaystyle \int\limits^9_5 {\frac{1}{x^3}e^\big{4x^{-2}}} \, dx$

Step 2: Integrate Pt. 1

Identify variables for u-substitution.

Set u: $\displaystyle u = 4x^{-2}$
[u] Differentiate [Basic Power Rule, Derivative Properties]: $\displaystyle du = \frac{-8}{x^3} \ dx$
[Bounds] Switch: $\displaystyle \left \{ {{x = 9 ,\ u = 4(9)^{-2} = \frac{4}{81}} \atop {x = 5 ,\ u = 4(5)^{-2} = \frac{4}{25}}} \right.$

Step 3: Integrate Pt. 2

[Integral] Rewrite [Integration Property - Multiplied Constant]: $\displaystyle \int\limits^9_5 {\frac{1}{x^3}e^\big{4x^{-2}}} \, dx = \frac{-1}{8}\int\limits^9_5 {\frac{-8}{x^3}e^\big{4x^{-2}}} \, dx$
[Integral] U-Substitution: $\displaystyle \int\limits^9_5 {\frac{1}{x^3}e^\big{4x^{-2}}} \, dx = \frac{-1}{8}\int\limits^{\frac{4}{81}}_{\frac{4}{25}} {e^\big{u}} \, du$
[Integral] Exponential Integration: $\displaystyle \int\limits^9_5 {\frac{1}{x^3}e^\big{4x^{-2}}} \, dx = \frac{-1}{8}(e^\big{u}) \bigg| \limits^{\frac{4}{81}}_{\frac{4}{25}}$
Evaluate [Integration Rule - Fundamental Theorem of Calculus 1]: $\displaystyle \int\limits^9_5 {\frac{1}{x^3}e^\big{4x^{-2}}} \, dx = \frac{-1}{8} \bigg( e^\Big{\frac{4}{81}} - e^\Big{\frac{4}{25}} \bigg)$
Simplify: $\displaystyle \int\limits^9_5 {\frac{1}{x^3}e^\big{4x^{-2}}} \, dx = \frac{1}{8} \bigg( e^\Big{\frac{4}{25}} - e^\Big{\frac{4}{81}} \bigg)$

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

Unit: Integration

4 0

2 years ago

PLZ PLZ PLZZZZZZ HELP ME IMMEDIATLEY

earnstyle [38]

Answer:

×=64

I HOPE IT CAN HELP:(

8 0

2 years ago

Urgenttttt please I need it fast

dolphi86 [110]

Answer:

Below in bold.

Step-by-step explanation:

c) 3 x (9^2)^3/4 x ((81^3)^5/6

= 3 x 81^3/4 x 81^15/6

= 3 x 81^(3/4 + 15/6)

= 3 x 81^13/4

= 3 x 3^13

= 3^14

= 4,782,969.

f) (5x^-1y^2)^-2 / (25 x^2 y - 1)^2

= 5^-2 x^2y^-4 / 625 x^4y^-2

= 5^-2 x^-2 y^-2 / 5^4

= 5^-6 x^-2y^-2

= 0.000064x^-2y^-2.

5 0

2 years ago

Note: Enter your answer and show all the steps that you use to solve this problem in the space provide.

enot [183]

The value of x from the given equation is 6

<h3>Solving linear equation</h3>

Linear equation are equation that has a leading degree of 1. A linear expression is given as y =ax + b

Given the linear equation below;

7x = 42

We are to determine the value of x

Divide both sides by 7

7x/7 = 42/7

x = 6

Hence the value of x from the given equation is 6

Learn more on linear equation here: brainly.com/question/2030026

#SPJ1

6 0

1 year ago

There are 10 red marbles and 20 green marbles in a bag. Colleen says the ratio of red marbles to green marbels is 19 to 20. Frit

nadezda [96]

Fritz is correct, in that the ratio is 1:2

Think of the ratio as a division

10:20 = 10/20

When you divide 10 with 20, you will get a decimal (or simplified fraction)

10/20 = 0.5

0.5 = 50 percent, or 1:2

Fritz is correct, in that 1:2 is the ratio

hope this helps

6 0

3 years ago

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