# 4.1.237 AP calculus exam find area

• MHB
• karush
In summary: i was thinking that maybe there was a typo in the question and that 1-x^2 was supposed to be -1-x^2 but you got it right so kudos to you
karush
Gold Member
MHB
$\tiny{237}$
$\textsf{The total area of the region bounded by the graph of$f(x)=x\sqrt{1-x^2}$and the x-axis is}$
$$(A) \dfrac{1}{3}\quad (B) \dfrac{1}{3}\sqrt{2}\quad (C) \dfrac{1}{2}\quad (D) \dfrac{2}{3}\quad (E) 1$$
find the limits of integration if
$$f(x)=0 \textit{ then } x=-1,0,1$$
so we have a symetric graph about $y=x$ so
$$\displaystyle 2\left|\int_{0}^1 x\sqrt{1-x^2}\,dx\right| =2\left( -\frac{1}{3}\left(1-x^2\right)^{\frac{3}{2}} \right)\bigg|_{0}^1 =\dfrac{2}{3}\quad (D)$$ok hopefully this is the answer but I was alarmed how much time I spent on calculation
which will kill you on these exams even if you get the corrects answers.not real sure what the slam dunk method would be just from obersavation.

karush said:
$\tiny{237}$
$\textsf{The total area of the region bounded by the graph of$f(x)=x\sqrt{1-x^2}$and the x-axis is}$
$$(A) \dfrac{1}{3}\quad (B) \dfrac{1}{3}\sqrt{2}\quad (C) \dfrac{1}{2}\quad (D) \dfrac{2}{3}\quad (E) 1$$
find the limits of integration if
$$f(x)=0 \textit{ then } x=-1,0,1$$
so we have a symetric graph about $y=x$ so
$$\displaystyle 2\left|\int_{0}^1 x\sqrt{1-x^2}\,dx\right| =2\left( -\frac{1}{3}\left(1-x^2\right)^{\frac{3}{2}} \right)\bigg|_{0}^1 =\dfrac{2}{3}\quad (D)$$ok hopefully this is the answer but I was alarmed how much time I spent on calculation
which will kill you on these exams even if you get the corrects answers.not real sure what the slam dunk method would be just from obersavation.
Looks good to me, although since you didn't mention what method you used to integrate. A simple substitution $$u = 1 - x^2$$ looks doable.

Also, this graph is not symmetric. It is antisymmetric.

-Dan

ok its not mirrored
I think some have called it symeteric about origin?

the integral is also a table reference but nobody could remember all of those

Mahalo

"From observation" you should immediately see the "$$1- x^2$$" inside the square root and the "x" outside the root and think "Aha, I can let $$u= 1- x^2[/tex[ so that [tex]dx= -2xdx$$ and I have the 'x' to give me 'xdx'!"

HallsofIvy said:
"From observation" you should immediately see the "$$1- x^2$$" inside the square root and the "x" outside the root and think "Aha, I can let $$u= 1- x^2[/tex[ so that [tex]dx= -2xdx$$ and I have the 'x' to give me 'xdx'!"

total awesome...

## 1. What is the format of the 4.1.237 AP calculus exam?

The 4.1.237 AP calculus exam is a standardized test that consists of multiple-choice questions, free-response questions, and a calculator portion. It covers topics such as limits, derivatives, and integrals.

## 2. How is the area found on the 4.1.237 AP calculus exam?

The area is found by using various integration techniques, such as the fundamental theorem of calculus, substitution, and integration by parts. The exam may also require students to use geometric formulas to find area.

## 3. Are there any specific strategies for finding area on the 4.1.237 AP calculus exam?

Yes, it is important for students to understand the concepts and techniques of integration, as well as practice solving various types of area problems. It is also helpful to carefully read and analyze the given problem, and to check for any special conditions or restrictions.

## 4. Can a calculator be used on the 4.1.237 AP calculus exam to find area?

Yes, a calculator is allowed on the exam and can be used to aid in finding area. However, students should also be able to solve area problems without a calculator, as some questions may not allow the use of one.

## 5. How can I prepare for the 4.1.237 AP calculus exam and its area-related questions?

Aside from studying and practicing integration techniques, it is also helpful to review geometric formulas and familiarize yourself with the types of area problems that may appear on the exam. Taking practice tests and seeking assistance from a teacher or tutor can also improve preparation for the exam.

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