1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Strike441 [17]
3 years ago
7

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

Mathematics
1 answer:
kicyunya [14]3 years ago
4 0

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:

<u>Calculus</u>

Differentiation

  • Derivatives
  • Derivative Notation

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

Basic Power Rule:

  1. f(x) = cxⁿ
  2. 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:

<u>Step 1: Define</u>

<em>Identify</em>

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

<u>Step 2: Integrate Pt. 1</u>

<em>Identify variables for u-substitution.</em>

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

<u>Step 3: Integrate Pt. 2</u>

  1. [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
  2. [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
  3. [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}}
  4. 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)
  5. 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

You might be interested in
PLEASE HELP.........
BlackZzzverrR [31]
<h3>Answer:  Choice C.   |x+3| < 5</h3>

=======================================================

Explanation:

Let's go through each answer choice and solve for x

----------------------------------------------------------------------

Choice A

|x+3| < -5

This has no solutions because |x+3| is never negative. It is either 0 or positive. Therefore, it can never be smaller than -5. So we can rule this out right away.

----------------------------------------------------------------------

Choice B

|x+8| < 2

-2 < x+8 < 2 .... see note below

-2-8 < x+8-8 < 2-8 ... subtract 8 from all sides

-10 < x < -6

We will have a graph where the open circles are at -10 and -6, with shading in between. This does not fit the original description. So we can rule this out too.

----------------------------------------------------------------------

Choice C

|x+3| < 5

-5 < x+3 < 5 .... see note below

-5-3 < x+3-3 < 5-3 .... subtracting 3 from all sides to isolate x

-8 < x < 2

We found our match. This graph has open circles at -8 and 2, with shading in between. The open circles indicate to the reader "do not include this value as a solution".

----------------------------------------------------------------------

note: For choices B and C I used the rule that |x| < k turns into -k < x < k where k is some positive number. For choice A, we have k = -5 which is negative so this formula would not apply.

7 0
4 years ago
What is the sale price of a bag of potato chips priced 4 and the sale 25% off?
Svet_ta [14]

Answer:

C: $3

Step-by-step explanation:

I think you're saying that the chips cost $4, so that's what I'm going with.

You can think of 25% as 1/4 of the whole. So if you divide 4 by 4, you get 1, so that means that 1/4 of the price is 1.

Now you can subtract 1 from 4 : 4-1= $3

Hope that helps!

4 0
3 years ago
A cricular arena is lit by 5 lights equally spaced around the perimeter of the arena. What is the measure of each angle formed b
Kitty [74]

Answer:

108°

Step-by-step explanation:

Suppose that circle with center A is a circular arena. Points B, C, D, E and F are 5 lights. These 5 points form regular pentagon (because these 5 lights are equally spaced around the perimeter of the arena).

The sum of all interior angles of pentagon can be calculated using following formula

(n-2)\cdot 180^{\circ},\\ \\(5-2)\cdot 180^{\circ}=3\cdot 180^{\circ}=540^{\circ}

All interior angles in regular pentagon are of equal measure, so

\dfrac{540^{\circ}}{5}=108^{\circ}

Thus, the measure of each angle formed by the lights on the perimeter is 108°.

7 0
4 years ago
Please help I will Mark brainilist
Alexxx [7]
The lowest number each sister would get is 3 pieces of jewelry each, when y=2
4 0
3 years ago
Felicity bought 3 shirts for $15 each and a pair of shoes for $25. Felicity used this equation to find x, the amount of money sh
torisob [31]

Answer:

x= 70

Step-by-step explanation:

In this question you have to use BODMAS. This indicates that you have to do the equation in the brackets first. Therefore, 3x15= 45. Then you add 25, which will give you 70.

8 0
2 years ago
Read 2 more answers
Other questions:
  • What is the definition of csc θ ?
    11·1 answer
  • Use an area model to solve. 1 3/4 X 2 1/2
    8·1 answer
  • True or False? Explain your choice.<br><br> 1, 2, 3, 6, 9, and 18 are all the factors of 18.
    13·2 answers
  • a canadian goose migrated at a steady rate of 4 miles every 7 minutes. find the slope of the graph and describe what it means in
    8·1 answer
  • Write 0.04 in two forms. Fraction and percentage out of 100
    12·2 answers
  • What in between 7/16 and 9/16
    13·1 answer
  • What is 4 divided by 1/8
    7·1 answer
  • What is the value of x?
    14·2 answers
  • Which power does not have a value of 64?
    10·1 answer
  • Question on picture urgent ​
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!