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
lisov135 [29]
3 years ago
9

Find the indefinite integrals, if possible, using the formulas and techniques you have studied so far in the text.(a) 11 x4 dxTh

is integral can be evaluated using the basic integration rules.This integral cannot be evaluated using the basic integration rules. (b) 8x1 x4 dxThis integral can be evaluated using the basic integration rules.This integral cannot be evaluated using the basic integration rules. (c) 3x31 x4 dxThis integral can be evaluated using the basic integration rules.This integral cannot be evaluated using the basic integration rule
Mathematics
1 answer:
hoa [83]3 years ago
6 0

Answer:

a) This integral can be evaluated using the basic integration rules. \int 11x^{4}dx = \frac{11}{5} x^{5}+C

b) This integral can be evaluated using the basic integration rules. \int 8x^{1}x^{4}dx=\frac{4}{3}x^{6}+C

c) This integral can be evaluated using the basic integration rules. \int 3x^{31}x^{4}dx=\frac{x^{36}}{12}+C

Step-by-step explanation:

a) \int 11x^{4}dx

In order to solve this problem, we can directly make use of the power rule of integration, which looks like this:

\int kx^{n}=k\frac{x^{n+1}}{n+1}+C

so in this case we would get:

\int 11x^{4}dx=11 \frac{x^{4+1}}{4+1}+C

\int 11x^{4}dx=11 \frac{x^{5}}{5}+C

b) \int 8x^{1}x^{4}dx

In order to solve this problem we just need to use some algebra to simplify it. By using power rules, we get that:

\int 8x^{1}x^{4}dx=\int 8x^{1+4}dx=\int 8x^{5}dx

So we can now use the power rule of integration:

\int 8x^{5}dx=\frac{8}{5+1}x^{5+1}+C

\int 8x^{5}dx=\frac{8}{6}x^{6}+C

\int 8x^{5}dx=\frac{4}{3}x^{6}+C

c) The same applies to this problem:

\int 3x^{31}x^{4}dx=\int 3x^{31+4}dx=\int 3x^{35}dx

and now we can use the power rule of integration:

\int 3x^{35}dx=\frac{3x^{35+1}}{35+1}+C

\int 3x^{35}dx=\frac{3x^{36}}{36}+C

\int 3x^{35}dx=\frac{x^{36}}{12}+C

You might be interested in
Ron made 3 pitchers of lemonade to sell at a lemonade stand. The cost of making the lemonade is 50 cents per pitcher of lemonade
julia-pushkina [17]

Answer:

3.90 I think.

Step-by-step explanation:

first, 15×36. then subtract 50 three times.

6 0
2 years ago
Read 2 more answers
A sphere has a diameter of 14 ft. What is its surface​ area? The surface area of the sphere is ft squared. ​(Type an exact answe
-BARSIC- [3]

Answer:

The Formula is 4 x Pi x Radius Squared . surface area of sphere = 4 x pi x radius x radius where "x" indicates multiplication and pi = approximately 3.141592654 4 * pi * r^2

Step-by-step explanation:

4 0
3 years ago
Which algebraic expression represents the phrase "six less than a number"?
elixir [45]

Answer:

x-6

Step-by-step explanation:

We can let the 'number' in the expression be equal to x. Something 6 less than x would x minus 6, or x-6.

4 0
2 years ago
Read 2 more answers
Plzzzz I will give you 100 points plzzz
kirza4 [7]

Answer: x < 8/9


Step-by-step explanation:

The equation is 4 * (2x +1) * 4.5 = 50, since the volume is found by multiplying the length, width, and height together, and the =50 part is because our volume can't go above 50 cubic units.


We can simplify 4 * (2x+1) * 4.5 by multiplying 4 and 4.5, which is 18, and then multiplying both 2x and 1 by 18. We get 36x + 18, and we put in the =50, so it is 36x+18=50.

Next, we can subtract 18 from both sides of the equation, giving us 36x = 32.

We then divide the equation by 36 so that we have the x by itself, and we get x = 32/36, which can be simplified to 8/9.


What we're left with is x = 8/9, meaning plugging in 8/9 for the equation would give us 50. However the problem says that the volume must be below 50, so our actual answer is x < 8/9.

7 0
3 years ago
Read 2 more answers
Rewrite (2x + 8) + 4 using the associative property. Then simplify.
skelet666 [1.2K]

Answer:

2x + 12

Step-by-step explanation:

Example of Associative Property Addition:

a + (b+c) = b + (a+c)

Now, implement it to the given expression:

(2x+8) + 4 = 2x + (8+4)

That simplifies to:

2x + 12

4 0
3 years ago
Read 2 more answers
Other questions:
  • Solve x/48 = 5/6 using two different strategies.
    9·1 answer
  • What is the median of the data shown in the box plot below?<br>A:23<br>B:28<br>C:30<br>D:35​
    10·2 answers
  • Write the equation of a line with slope 3 and y-intercept −3.<br><br> PLS I NEED ASAP
    15·1 answer
  • A fully-loaded truck is carrying grain to a storage silo. if the truck is 8 feet wide, 40 feet long, and 4 feet deep, how many b
    12·2 answers
  • Show all your work. Indicate clearly the methods you use, because you will be scored on the correctness of your methods as well
    8·1 answer
  • 3. the quotient of -9 and y
    11·1 answer
  • PLEASE LOOK AT PICTURE! WHOEVER HAD CORRECT ANWSER I WILL MARK BRAINIEST!!!
    9·2 answers
  • Help plsssssssssssss???
    15·2 answers
  • Which statement(s) give advantages or disadvantages of systematic random sampling? Check all that apply.
    11·1 answer
  • The diameter of a basketball rim is 45 centimeters. What is the measurements around the rim. Use 3.14 for π.
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!