# Calculus - Urgent!!!

posted by .

In case this looks familiar, yes, it is a repost. I really need help.

Find the anti-derivitive of
f(x)= x^3(x-2)^2.

Multiple choice gives me the options:
A: 1/6 x^6 - 4/5 X^5 + x^4 + C
B: 1/6 x^6 - 4/5 X^5 + 1/4 x^4 + C
C: x^6 - X^5 + x^4 + C
D: x^5 - 4x^4 + 4x^3 + C

I got as far as factoring the original equation into x^5 - 4x^4 + 4x^2. I was told I need to integrate the function. I'm not sure how to do that. My book is NOT clear or helpful, and hasn't been for this whole calculus course.

Please help me understand how my equation can possibly be one of the equations in the A-B-C-D options.

Thank you and God bless you for taking the time to read this, let alone help!

• Calculus - Urgent!!! -

Yes, you need to integrate the function.
I am sure antiderivatives and integration are in your text.

first multiply it out
x^3(x-2)^2 = x^3 (x^2 - 4 x + 4)
= x^5 -4x^4 + 4 x^3 (note that last x^3)

now in general the integral of x^n dx is (1/n+1)x^(n+1)
so for example the integral of x^2dx is
(1/3)x^3 + a constant C
so here we have
(1/6)x^6 -(4/5)x^5 + x^4 + C

• Calculus - Urgent!!! -
• Calculus - Urgent!!! -

• Calculus - Urgent!!! -

Ah, thank you so much. Those are very helpful. Yes, anti-derivatives and integrals are in my text, but it is explained in one paragraph. Thanks again!

• For: "in Need of Help" -

Now do you see what I meant about switching names in my earlier post
http://www.jiskha.com/display.cgi?id=1335474065

Both Damon and I spent time answering the same question.

• Calculus - Urgent!!! -

I apologize. I didn't see the earlier post, but it won't happen again. Sorry to the both of you.

## Similar Questions

1. ### education

explain what school choice options are available. Do you feel having school choice options is a benefit to parents and students?
2. ### Calc I

Yes I was trying to find the range y = (x^2 -4)/(x^2 - x -12) ok using 2(4 +/- sqrt(15) ) sorry I forgot the minus in the derivitive but ya that makes sense but however I need three critical values that only gives me graph it and you'll …
3. ### Stats

An instructor gives a test with 20 multiple choice questions. There are 4 responses per questions and only one choice correct. The test also has 30 True/False questions. Determine the probability a student randomly guessing on all …

find the antiderivative of f(x) = x^3(x-2)^2 I factored this out and got x^5-4x^4+4x^2 I'm supposed to integrate this. I don't know how. Someone help me please?
5. ### AlgebraB

I have somemultiple choice questions that I need help with. Question 1 Find the measure of <AEB for m<BEC = 127° These are my options: 127° 254° 106° 53° Question 2 Name the alternate interior angle to <7: These are the …
6. ### Calculus

Find the anti derivative of u^-2(1-u^2+u^4)du. Need steps so I can try to grasp this. Thanks. I couldn't figure out how to write the anti deriv. symbol but it is in front on the u^-2. Thanks
7. ### Calculus

Find the anti derivative of the following: 1. u^-2(1-u^2+u^4)du 2. (sqrt(x)+ 3/x - 2e^(x))dx The anti derivative symbol is in front of the equations. Also need help on find f(x) so that it satisfies f'(x) = 1+e^x+1/x and f(1) = 3+e. …
8. ### Calculus Please Need Urgent :/

Find the most general antiderivative of f(x)=–8e^x–6secant^2(x) where -pi/2<x<pi/2 Note: Any arbitrary constants used must be an upper-case "C". F(x)=?
9. ### Math

12+4n/3 = 8 Not multiple choice.. trying to find n. My answer is 7 9a - 3(a -6) = -6 Not multiple choice.. I'm not quite sure how to do this The width of a rectangle is 6 in. less than its length. The perimeter is 68 in. What is the …
10. ### Math

Each day Julia's math Teacher gives class a warm up qs. It's true/false 20% of the times and multiple choice 80% . Julia gets 70% on true false correct and 90% on multiple choice correct. Julia answered today's question correctly. …

More Similar Questions