4.2.5 AP Calculus Exam int of e

So the integral becomes \int_1^2 du.In summary, we changed the variable from x to u, which also changed the limits of integration from (1, 4) to (1, 2). This was done because when changing variables, every reference to the old variable must be changed to the new one.
  • #1
karush
Gold Member
MHB
3,269
5
View attachment 9321

calculator returned this but know sure why
$\displaystyle2 \int _1^2e^udu$
note there might be a duplicat of this post ?
 

Attachments

  • 298.PNG
    298.PNG
    5.5 KB · Views: 104
Physics news on Phys.org
  • #2
$u=\sqrt{x} \implies du = \dfrac{1}{2\sqrt{x}} \, dx$

\(\displaystyle {\color{red}{2}} \int_1^4 \frac{e^{\sqrt{x}}}{{\color{red}{2}} \sqrt{x}} \, dx = 2 \int_1^2 e^u \, du\)
 
  • #3
skeeter said:
$u=\sqrt{x} \implies du = \dfrac{1}{2\sqrt{x}} \, dx$

\(\displaystyle {\color{red}{2}} \int_1^4 \frac{e^{\sqrt{x}}}{{\color{red}{2}} \sqrt{x}} \, dx = 2 \int_1^2 e^u \, du\)

Why would that change the limits,?
 
  • #4
karush said:
Why would that change the limits,?
The original integral over x was done over an interval (1, 4).

When we changed the variable to u(x) we are no longer integrating over x. We are now integrating over u. So the interval changes to (1, 2).

-Dan
 
  • #5
When you change from x to u, every reference to "x" has to change to a reference to "u". "[tex]\int_1^4 dx[/tex]" means we are taking the integral fron x= 1 to x= 4. We have to change that to u. When x= 1, [tex]u= \sqrt{1}= 1[/tex] and when x= 4, [tex]u= \sqrt{4}= 2[/tex].
 

FAQ: 4.2.5 AP Calculus Exam int of e

What is the 4.2.5 AP Calculus Exam?

The 4.2.5 AP Calculus Exam is a standardized test administered by the College Board to assess a student's understanding and ability in the subject of Calculus. It is typically taken by high school students who have completed a Calculus course.

What does "int of e" mean on the AP Calculus Exam?

"Int of e" refers to the integration of the mathematical constant "e" in a Calculus problem. Integration is a fundamental concept in Calculus that involves finding the area under a curve.

What topics are covered on the 4.2.5 AP Calculus Exam?

The 4.2.5 AP Calculus Exam covers a wide range of topics in Calculus, including limits, derivatives, integrals, applications of derivatives and integrals, and the Fundamental Theorem of Calculus. It also includes questions on algebraic, trigonometric, exponential, and logarithmic functions.

How long is the 4.2.5 AP Calculus Exam?

The 4.2.5 AP Calculus Exam is approximately 3 hours and 15 minutes long. It is divided into two sections, with a 45-minute multiple-choice section and a 1 hour and 45 minute free-response section.

What is a passing score on the 4.2.5 AP Calculus Exam?

A passing score on the 4.2.5 AP Calculus Exam is typically considered to be a 3 or higher, on a scale of 1-5. However, this may vary depending on the college or university a student is applying to and their individual standards for credit or placement.

Similar threads

Replies
6
Views
2K
Replies
1
Views
982
Replies
4
Views
2K
Replies
4
Views
1K
Replies
1
Views
1K
Replies
3
Views
1K
Replies
5
Views
1K
Back
Top