Kindergarten Homework: 10S t^3 dt=f(x)

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Homework Help Overview

The discussion revolves around evaluating the integral of the function t^3 and its relationship to the function f(x). The original poster seeks clarification on the differentiation of the integral expression.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • The original poster attempts to differentiate the integral directly, leading to confusion about the correct expression for f'(x). Some participants suggest finding the indefinite integral first, then evaluating it before differentiation.

Discussion Status

Participants are exploring the steps involved in integrating and differentiating the function. Guidance has been offered regarding the proper sequence of operations, and there is acknowledgment of learning from the discussion.

Contextual Notes

The original poster expresses uncertainty about their understanding, indicating a need for clarification on the differentiation process following integration.

beanryu
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HI people, this will be kindergarden homework for you guys. PLease help! THANKS a lot!

S=integral sign

10
S t^3 dt=f(x)
x

f'(x)=?
I say f'(x)=t^3, but it's not correct. WHY?
 
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First, find the indefinite integral of t3 dt, then evaluate it from t=x to t=10. Only after you've completed that can you differentiate the resultant expression with respect to x.

- Warren
 
so the indefinite integral of t^3 dt is t^4/4

then evaluate it from t=x to t=10

10^4/4-x^4/4

then differentiate this expression

0-x^3

it's correct!... I am dumb THANX a lot fOR The fAsT repLY !
 
Last edited:
You're not dumb at all. See, you just learned something. :)

- Warren
 

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