Solve Integration Problem Homework: Jennie

• JenniferBlanco
In summary, the conversation discusses finding the constant c in order to determine the function f(x) using the given equations and information. Through the use of integration and substitution, the values of a and b are determined to be 12 and -6 respectively, and the final function is found to be f(x) = 4x^3 - 3x^2 + 10.
JenniferBlanco

Homework Statement

I don't know how to make the integral sign so I am took a picture of the question.

http://img99.imageshack.us/img99/4139/mathquestional7.jpg

Homework Equations

Equations are located in the above img.

The Attempt at a Solution

I first integrated the first derivative and got -

(ax^3)/3 + (bx^2)/2

plugged in 1 and got -

6=a + b

Then I got the second derivative --> 2ax +b and plugged in f''(1) and got: 18 = 2a +b

Using both the equations, I figured out that:
a=12
b=-6

how do I find the contant c to get f(x)?-Jennie

Last edited by a moderator:
JenniferBlanco said:
how do I find the contant c to get f(x)?
By using (iii)?

I am assuming you meant f(x) = (ax^3)/3 + (bx^2)/2 + c.

I tried using (iii) and this is what I got -

f(x) = 4x^3 -3x^2 + c

then I plugged in 2 and 1 and got -

(32-12+c) - (4-3+c) = 18

but then c will cancel out.

I am sure I am doing this wrong. please guide me

What do you get when you integrate 4x^3 -3x^2 + c without limits?

x^4 - x^3 + cx

Shouldn't it be x^4-x^3+cx?

yes, i edited it before you replied.

What do you get for x=1? For x = 2?

when x=1 then I got c
when x=2 then I got 8+2c

Do you think you can use (iii)?

Thank you!

so,

(8 +2c) - c = 18
and c = 10

that gives me--> f(x)= 12x^2 - 6x + 10

Do you mean f(x) = 4x^3 -3x^2 + 10?

aaah yes. I was writing it down and was wondering how 6=18.

Sorry for the error and Thanks for the help. :)

What is "Solve Integration Problem Homework: Jennie"?

"Solve Integration Problem Homework: Jennie" is a specific homework assignment that involves solving integration problems. It is likely assigned by a teacher or professor in a math or science course.

Why is integration important in science?

Integration is important in science because it allows us to find the total or cumulative effect of a changing quantity. This is useful in fields like physics, chemistry, and biology where we often need to calculate things like total distance traveled, total energy expended, or total population growth.

How do I solve an integration problem?

To solve an integration problem, you will need to use integration techniques such as substitution, integration by parts, or trigonometric substitution. You will also need to have a good understanding of the properties of integrals and how to manipulate them algebraically.

What are some tips for solving integration problems?

Some tips for solving integration problems include: identifying the appropriate integration technique to use, carefully setting up the problem by identifying the limits of integration and the integrand, checking your answer using differentiation, and practicing regularly to become more familiar with the process.

Is there software or tools that can help me solve integration problems?

Yes, there are many software programs and online tools that can help you solve integration problems. Some popular options include Wolfram Alpha, Symbolab, and Desmos. These tools can provide step-by-step solutions and also allow you to check your work.

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