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
Annette [7]
3 years ago
12

Consider the curve defined by the equation y=6x2+14x. Set up an integral that represents the length of curve from the point (−2,

−4) to the point (1,20).
Mathematics
1 answer:
torisob [31]3 years ago
5 0

Answer:

32.66 units

Step-by-step explanation:

We are given that

y=6x^2+14x

Point A=(-2,-4) and point B=(1,20)

Differentiate w.r. t x

\frac{dy}{dx}=12x+14

We know that length of curve

s=\int_{a}^{b}\sqrt{1+(\frac{dy}{dx})^2}dx

We have a=-2 and b=1

Using the formula

Length of curve=s=\int_{-2}^{1}\sqrt{1+(12x+14)^2}dx

Using substitution method

Substitute t=12x+14

Differentiate w.r t. x

dt=12dx

dx=\frac{1}{12}dt

Length of curve=s=\frac{1}{12}\int_{-2}^{1}\sqrt{1+t^2}dt

We know that

\sqrt{x^2+a^2}dx=\frac{x\sqrt {x^2+a^2}}{2}+\frac{1}{2}\ln(x+\sqrt {x^2+a^2})+C

By using the formula

Length of curve=s=\frac{1}{12}[\frac{t}{2}\sqrt{1+t^2}+\frac{1}{2}ln(t+\sqrt{1+t^2})]^{1}_{-2}

Length of curve=s=\frac{1}{12}[\frac{12x+14}{2}\sqrt{1+(12x+14)^2}+\frac{1}{2}ln(12x+14+\sqrt{1+(12x+14)^2})]^{1}_{-2}

Length of curve=s=\frac{1}{12}(\frac{(12+14)\sqrt{1+(26)^2}}{2}+\frac{1}{2}ln(26+\sqrt{1+(26)^2})-\frac{12(-2)+14}{2}\sqrt{1+(-10)^2}-\frac{1}{2}ln(-10+\sqrt{1+(-10)^2})

Length of curve=s=\frac{1}{12}(13\sqrt{677}+\frac{1}{2}ln(26+\sqrt{677})+5\sqrt{101}-\frac{1}{2}ln(-10+\sqrt{101})

Length of curve=s=32.66

You might be interested in
5*45+6856x=8x+65x+76x
Brut [27]

Answer:

0.033547          I think

Step-by-step explanation:

4 0
3 years ago
What is the answer to this question about dividing fractions5 5⁄6 ÷ 3 2⁄4=
Lady_Fox [76]

[~Answer~] (4.):
<em>Hello there! I'm Avery, and I'm here to help you! I mostly believe the answer </em><em>is 1 2/3


+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
</em>

[~Answer Explanation~]:

First:

Convert any mixed numbers to fractions.

Reduce fractions where possible.

Then your initial equation becomes:

356÷72

Applying the fractions formula for division,

=35×26×7

=70/42

Simplifying 70/42, the answer is

=1 2/3

+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
[~Last Messages~]:

Okay, I really hope my answer is correct.

I am truly sorry if it's wrong :(

Have a great morning, afternoon, or night. <333

[-!AveryIsSomeHowAlive!-]

3 0
1 year ago
How much money did tommys class collect
Anastaziya [24]
B. 7.50 is the answer
6 0
3 years ago
Expressions  with mixed operations Evaluate.<br> 2.3+3.7-2/27.5-4*5.625
masya89 [10]
2.3+3.7-2/27.5-4*5.625. use pedmas.
=appromaxietly -16.57

5 0
3 years ago
What is the slope of a line that is parallel to the line represented by the equation : y = 5x - 3?
Lerok [7]

Answer:

5

Step-by-step explanation:

This line equation is in  y = mx + b form    m will be the slope

 m = 5     parallel line will have same slope  = 5  

5 0
2 years ago
Other questions:
  • How to solve system of equations khan academy?
    13·1 answer
  • PLEASE ANSWER FAST
    7·2 answers
  • Help me please thank you
    13·2 answers
  • Can someone check over this? And explain if it's wrong?
    14·1 answer
  • A cube has the volume of 216 in3 determine the area of on face of the cube
    13·1 answer
  • Solve by substitution 2y=x+1 -2x-y=7
    8·1 answer
  • Find the quotient. Round to the nearest hundredth,5,434 divided by 12
    14·1 answer
  • Triangle KMZ~ triangle KDH; find x
    14·1 answer
  • Use the slope formula to find the slope of the line that passes through the points (6,3) and (9,8).
    11·1 answer
  • 1.2+3x6= <br> 2.4(8-3)=<br> 3.7+8(3+2)= <br> 4. (6-5)+(8x10)=
    7·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!