Calculus BC

Test Preparation
1

<p>Hi, I have two problems from the Barron's AP Calculus practice test that I do not understand. Can anyone help me?
problem 1:
For the substituion x = sin(theta), which integral is equivalent to the integral of [sqrt(1+(x^2))/x] dx from 0 to 1?
A. integral of cot(theta) d(theta) from pi/4 to 0
B. integral of cot(theta) d(theta) from 0 to pi/2
C. integral of [(cos(theta))^2]/sin(theta) d(theta) from 0 to pi/2
D. integral of [(cos(theta))^2]/sin(theta) d(theta) from 0 to 1
E. none of these
My answer: B
Book's answer: C
can someone please explain what I had gotten wrong?</p>

<p>problem 2:
Water is leaking from a tank at the rate of R(t) = 5 arctan (t/5) gallons per hour, where t is the number of hours since the leak began. How many gallons will leak out during the first day?
A. 7
B. 82
C. 124
D. 141
E. 164
My answer: 75.28 (not in the choices)</p>

2

<p>For problem no. 1, are you sure it's not 1-x^2 inside the radical?</p>

3

<p>Umm, I'm sorry, it is 1-x^2. Thank you!</p>

4

<p>for prooblem number 2 I just tried plugging 24 in as t and it came up as 6.827. Is 7 the right answer for that one?</p>

<p>actually I think it might be the integral of R(t) from 0 to 24. That came out to 124.102 or 124.</p>