# 303 AP calculus int with initial value

• MHB
• karush
In summary, "303 AP calculus int with initial value" is a course designed for advanced placement high school students that covers integral calculus, with a focus on solving problems involving initial values. The course covers topics such as finding antiderivatives, definite and indefinite integrals, and techniques for solving initial value problems. The target audience for this course is advanced high school students with a strong foundation in mathematics, and it is also suitable for those looking to earn college credit through the AP program. Prerequisites for the course include completion of a precalculus course or similar advanced math course, as well as a strong understanding of algebra and basic calculus concepts. To prepare for the course, it is recommended to review basic calculus concepts and practice solving problems involving
karush
Gold Member
MHB
View attachment 9383
ok image to avoid typo... try to solve before looking at suggested solutions

so then we have first $$\displaystyle y=\int 2\sin x \,dx=-2cos x +C$$ if $y(\pi)=1$
then
$$y(\pi)=-2cos(\pi) +C=1$$
then
$$2cos(\pi)+1=C$$
and
$$2(-1)+1=C=-1$$
and finally
$$y=-2cos{x}-1$$
which is $\textbf{(E)}$
ok I think you could do this by observation if you are careful with signs

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$$\displaystyle \frac{dy}{dx}=2sinx$$
$$\displaystyle y=-2cosx+C$$
$$\displaystyle y(\pi)=1$$
$$\displaystyle -2cos\pi+C=1$$
$$\displaystyle -2(-1)+C=1$$
$$\displaystyle 2+C=1$$
$$\displaystyle C=-1$$
$$\displaystyle y=-cosx+C$$
$$\displaystyle y=-cosx-1$$
I got E as the answer.

## 1. What is "303 AP calculus int with initial value"?

"303 AP calculus int with initial value" is a specific course in the field of calculus that focuses on the application of integration to solve problems involving initial values. It is typically taken by high school students who are preparing to take the Advanced Placement (AP) Calculus exam.

## 2. What topics are covered in "303 AP calculus int with initial value"?

The topics covered in "303 AP calculus int with initial value" include indefinite and definite integrals, applications of integration such as finding areas and volumes, and using integration to solve problems involving initial values, such as differential equations.

## 3. What is the difference between "303 AP calculus int with initial value" and regular calculus courses?

The main difference between "303 AP calculus int with initial value" and regular calculus courses is the focus on initial values. While regular calculus courses cover a wide range of topics in both differentiation and integration, "303 AP calculus int with initial value" specifically emphasizes the application of integration to solve problems involving initial values.

## 4. What are the prerequisites for taking "303 AP calculus int with initial value"?

The prerequisites for taking "303 AP calculus int with initial value" vary depending on the school or institution offering the course. However, it is typically recommended that students have a strong understanding of algebra, geometry, and basic calculus concepts such as derivatives and antiderivatives.

## 5. How can "303 AP calculus int with initial value" be useful in real life?

The skills and concepts learned in "303 AP calculus int with initial value" can be useful in a variety of real-life situations. For example, understanding integration and initial values can help with financial planning, predicting population growth, and analyzing data in fields such as economics, physics, and engineering.

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