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
Andreas93 [3]
3 years ago
12

Evaluate the integral. (Assume a ≠ b. Remember to use absolute values where appropriate. Use C for the constant of integration.)

5 (x + a)(x + b) dx
Mathematics
1 answer:
Bess [88]3 years ago
4 0

Answer:

<u><em>F(x)= 5*[\frac{x^{3} }{3} + (a*b)*\frac{x^{2} }{2} + a*b*x + C.</em></u>

Step-by-step explanation:

<u><em>First step we aplicate distributive property to the function.</em></u>

<u><em>5*(x+a)*(x+b)= 5*[x^{2}+x*b+a*x+a*b]</em></u>

<u><em>5*[x^{2}+x*(b+a)+a*b]= f(x), where a, b are constant and a≠b</em></u>

<u><em>integrating we find ⇒∫f(x)*dx= F(x) + C, where C= integration´s constant</em></u>

<u><em>∫^5*[x^{2}+x*(a+b)+a*b]*dx, apply integral´s property</em></u>

<u><em>5*[∫x^{2}dx+∫(a*b)*x*dx + ∫a*b*dx], resolving the integrals </em></u>

<u><em>5*[\frac{x^{3} }{3} + (a*b)*\frac{x^{2} }{2} + a*b*x</em></u>

<u><em>Finally we can write the function F(x)</em></u>

<u><em>F(x)= 5*[\frac{x^{3} }{3} + (a*b)*\frac{x^{2} }{2} + a*b*x ]+ C.</em></u>

You might be interested in
What is the rate and unit rate for 5pencils for 11 dollars?
Harrizon [31]
The unit rate is $2.20 for each pencil because 11 divided by 5 is 2.2
7 0
3 years ago
How many ways can the words in d-r-a-g-o-n-f-l-y be arranged
GarryVolchara [31]

Answer:

362880 ways

Step-by-step explanation:

The word dragonfly has 9 different letters.

So, to find how many ways this word can be arranged, we just need to calculate the factorial of 9:

First letter has 9 possibilities

Second letter has 8 possibilities (one used)

Third letter has 7 possibilities (two used), and so on.

So the number of ways is:

9*8*7*6*5*4*3*2*1 = 362880 ways

7 0
3 years ago
For the arithmetic sequence 42, 32, 22, 12... find the 18th term.
Stella [2.4K]

Answer:

The18th term of the given sequence is -128

Explanation:

To find the 18th term of the sequence:

42, 32, 22, 12, ..., we need to find the nth term of the sequence first.

The nth term of a sequence is given be the formula:

T_n=a+(n-1)d

Where a is the first term, and d is the common difference.

Here, a = 42, d = 32 - 42 = -10

\begin{gathered} T_n=42+(n-1)(-10) \\ =42-10n+10 \\ T_n=52-10n \end{gathered}

To find the 18th terem, substitute n = 18 into the nth term

\begin{gathered} T_{18}=52-10(18) \\ =52-180 \\ =-128 \end{gathered}

7 0
1 year ago
dave and his sister picked out two pumpkins at the pumpkin patch. the pumpkins cost $0.47 per pound. davids pumpkin weighed 13.2
WINSTONCH [101]
Dave has 50 cents right now
4 0
4 years ago
Read 2 more answers
PLEASE HELP
Papessa [141]
<2,14>  thats the answer its complicated but i got it after the 2nd try 

3 0
3 years ago
Read 2 more answers
Other questions:
  • How to write 800+10+4 in standard form
    12·2 answers
  • Evaluate :cos 45 by sin 30 + cosec 30​
    13·2 answers
  • For the purpose of purchasing new baseboard and​ carpet, complete parts a and b below. a. Find the area and perimeter of the roo
    7·1 answer
  • Has to be evaluated in scientific notation
    9·1 answer
  • Square root of 80 minus the square root of 5
    9·1 answer
  • What is the answer to this question. Please give me the answer ASAP
    12·1 answer
  • Identify the form of the equation and two characteristics of the function's graph. y = –7x + 2 Group of answer choices Point-Slo
    5·1 answer
  • Under his cell phone plan, Owen pays a flat cost of $67.50 per month and $4 per gigabyte. He wants to keep his bill at $71.90 pe
    15·1 answer
  • Find the value of x and y.
    7·1 answer
  • . Solve the system of equations using the Elimination Method.
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!