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
Ivahew [28]
3 years ago
6

Find the most general antiderivative of the function. (Check your answer by differentiation. Use C for the constant of the antid

erivative.)
g(t) = 6 + t + t2/square root t
Mathematics
1 answer:
vredina [299]3 years ago
5 0

Answer:

6t + \frac{t^2}{2}+2/5t^{5/2} + C

Step-by-step explanation:

Given the expression;

g(t) = 6 + t + t²/√t

This can be rewritten as;

g(t) = 6 + t +t²/t^1/2

g(t) = 6 + t +t^{2-1/2}

g(t) = 6 + t +t^3/2

Integrate the result

\int\limits {(6 + t+t^{3/2}}) \, dt\\

Using the formula x^{n+1}/n+1

\int\limits {(6  + t+t^{3/2}}) \, dt\\ = 6t + \frac{t^2}{2}+\frac{t^{3/2+1}}{3/2 + 1} \\ = 6t + \frac{t^2}{2}+\frac{t^{5/2}}{5/2} \\= 6t + \frac{t^2}{2}+2/5t^{5/2} + C

You might be interested in
Which is the equation of the given line in slope-intercept form? (-1, 2) and (1, -4)
Natalka [10]
1. Find the slope using the slope formula.
\frac{2 - ( - 4)}{ - 1 - 1}  =  \frac{2 + 4}{ - 2}  =  -  \frac{6}{2}  =  -  \frac{3}{1}  =  - 3
2. Plug that slope and either point into an equation in slope-intercept form and solve for b.
2 =  - 3( - 1) + b \\ 2 = 3 + b \\  - 1 = b
3. Now write your answer as a slope-intercept form equation
y =  - 3x - 1
6 0
3 years ago
Read 2 more answers
Ella has $115. She wants to purchase a cell phone for $53 and spend the rest on music. Each music album costs $9. Write and solv
lana [24]
53 + 9x < 115
THE LESS THAN SYMBOL SHOULD HAVE A LINE UNDER IT!
3 0
3 years ago
HELPP MEEEEEE<br> Find the slope of this graph.
kati45 [8]

Answer:

that this 6+6

Step-by-step explanation:

78+90 look than

4 0
3 years ago
Read 2 more answers
A 50 foot ladder is set against the side of a house so that it reaches up 30 feet. If
Allisa [31]

Answer:

21.8

Step-by-step explanation:

7 0
3 years ago
What city was the first capital of the United States?​
Wewaii [24]

I believe New York City was the first capital of the US.

3 0
2 years ago
Read 2 more answers
Other questions:
  • What is the value of x when 14x=-2x
    8·2 answers
  • A pair of dice are rolled. What is the probability of rolling 4 or greater?
    15·1 answer
  • Use algebra to find the inverse of the function f(x)=3x^5+7
    15·1 answer
  • The length of a rectangle is four times it's width and has an area of 1024cm squared. Work out the width of the rectangle
    11·1 answer
  • If 6 people can paint a room in 36 minutes, how many people would it take to paint the room in exactly 24 minutes?
    12·1 answer
  • What is the slope and y-intercept of y=2/3x+2 ?
    8·1 answer
  • What is the value of x if 15 = 5x + 45 ?
    12·2 answers
  • -<br> -<br> What is the vertex of the quadratic function f(x) = (x - 6)(x + 2)?
    9·2 answers
  • Please help ASAP thank you
    7·1 answer
  • Use the vertical method to multiply (4a^3 - 2a + 3a^2 + 1) (4a3−2a+3a2+1) and (3 - 2a + a^2). (3−2a+a2). What would be the value
    9·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!