# 4.1.1 AP calculus Exam Int with U substitution

• MHB
• karush
In summary, we evaluated the integral $\displaystyle\int{\dfrac{{(1-\ln{t})}^2}{t} dt}$ and found that the correct answer is $a\quad {-\dfrac{1}{3}{(1-\ln{t})}^3+C}$. This was verified by taking the derivative of the answer. We used u substitution with $u=1-\ln{t}$ to simplify the integral.
karush
Gold Member
MHB
Evaluate $\displaystyle\int{\dfrac{{(1-\ln{t})}^2}{t} dt=}$

$a\quad {-\dfrac{1}{3}{(1-\ln{t})}^3+C} \\$
$b\quad {\ln{t}-2\ln{t^2} +\ln{t^3} +C} \\$
$c\quad {-2(1-\ln{t})+C} \\$
$d\quad {\ln{t}-\ln{t^2}+\dfrac{(\ln{t^3})}{3}+C} \\$
$e\quad {-\dfrac{(1-\ln{t^3})}{3}+C}$

ok we can either expand the numerator or go with u substitution $u=1-\ln{t}$

Just by intution I would quess the answer is (a)

substitution ...

and (a) is correct, verified by its derivarive

Since you titled this "int with u substitution" it looks like you have chosen substitution!

Yes, let u= 1- ln(t). Then du= -dt/t so the integral becomes
$\int u^2(-du)= -u^3/3+ C= -1/3(1- ln(t))^3+ C. That is (a) as you say. Well done! wow I was expecting about 6 steps (think you left off a \$ sign)

$\displaystyle\int u^2(-du)= -u^3/3+ C= -1/3(1- ln(t))^3+ C$

## What is the format of the 4.1.1 AP Calculus Exam Int with U substitution?

The 4.1.1 AP Calculus Exam Int with U substitution consists of a multiple-choice section and a free-response section. The multiple-choice section has 28 questions and is 1 hour and 45 minutes long. The free-response section has 6 questions and is 1 hour and 30 minutes long.

## What topics are covered in the 4.1.1 AP Calculus Exam Int with U substitution?

The 4.1.1 AP Calculus Exam Int with U substitution covers topics such as definite and indefinite integrals, u-substitution, and integration by parts. It also includes applications of integration, such as finding areas between curves and volumes of solids of revolution.

## How is the 4.1.1 AP Calculus Exam Int with U substitution scored?

The multiple-choice section of the 4.1.1 AP Calculus Exam Int with U substitution is scored on a scale of 1-5, with 5 being the highest score. The free-response section is scored on a scale of 0-9, with 9 being the highest score. These scores are then combined to give a final composite score.

## What is the best way to prepare for the 4.1.1 AP Calculus Exam Int with U substitution?

The best way to prepare for the 4.1.1 AP Calculus Exam Int with U substitution is to practice with past exams and review course materials. It is also helpful to work on problems that cover a variety of topics and to seek help from a teacher or tutor if needed.

## Are there any resources available to help with studying for the 4.1.1 AP Calculus Exam Int with U substitution?

Yes, there are many resources available to help with studying for the 4.1.1 AP Calculus Exam Int with U substitution. These include review books, online practice exams, and study guides. Your teacher or school may also have additional resources or study sessions available.

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