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]
2 years ago
7

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

Mathematics
1 answer:
kicyunya [14]2 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
the running aces card team won $548 playing in poker tournaments.The winnings were split evenly among the p players.How much mon
meriva

Answer:

\frac{548}{p}.

3 0
3 years ago
Read 2 more answers
The length of a rectangle is 2 ft shorter than 5 times its width, x. The area of the rectangle is less than 100 f12.
Ierofanga [76]

Answer:

A

Step-by-step explanation:

Area of rectangle  = length x width

length = 5x - 2

width = x

area = (5x - 2) × x

100 = 5x² - 2x

the width would be less than the area of the rectangle, thus the inequality sign to be used is <

5x² - 2x < 100

7 0
3 years ago
Use the distributive property to multiply the polynomials.
vova2212 [387]

Answer:

-30x^3+5x^2

Step-by-step explanation:

5 0
3 years ago
What is the slope? Loooook atttt the chartttt ✨
gavmur [86]

Answer:

m = 3/5

Step-by-step explanation:

Slope Formula: m=\frac{y_2-y_1}{x_2-x_1}

Step 1: Find 2 coordinates

(0, 80)

(-50, 50)

Step 2: Find slope <em>m</em>

m = (50 - 80)/(-50 - 0)

m = -30/-50

m = 3/5

8 0
3 years ago
Find the side of a square with area of 25 sq. ft
zheka24 [161]
The side of a square would be 5 because the square root of 25 is 5.
7 0
3 years ago
Read 2 more answers
Other questions:
  • What is ??? 5(m-n) It’s distributive property and simply it
    7·1 answer
  • Do question 14 plz if u do it thanks sooooooo much I keep on getting a decimal answer that is WRONG
    6·2 answers
  • Can someone PLEASEEEE help me with this I don’t understand how to do it
    5·1 answer
  • Who wanna be my tutor add my Instagram : laylarainn help a girl out ‍♀️
    13·2 answers
  • I need help on my homework .&gt;. What's the median, first quartile, third quartile, and interquartile range for the numbers 14,
    12·1 answer
  • Louis has three more quarter than dime in his pocket for a total of 1.80 which equation could be used to determine the number of
    9·2 answers
  • 2. The 120 sixth graders are going on a
    10·1 answer
  • Skate station charges a flat rate of $5.00 per day for skate rental plus $2.00 per hour of skating. If the number of hours is re
    13·1 answer
  • Cheryl borrowed $7,000 from her parents to purchase a car interest free. she makes one payment on the loan to her parents each m
    8·1 answer
  • Denis orders a large pizza for $16.50 plus $2 for each topping. Sheng orders a medium pizza for $13.25 plus $2 for each topping.
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!