Let R be the region in the first quadrant under the graph of y=1/sqrt(x) for 4</=x</=9.

Question

(a)Find the area of R.
I took the antideriative. Then, I plugged in the 9 and 4. I got 2.
(b) If the line x=k divides the region R into two regions of equal area, what is the value of k?
I don't know how to do this one.

Answer 1

your first answer is correct

for the second part set the two areas equal
so 2√x (from 4 to k) = 2√x (from k to 9)

2√k - 2√4 = 2√9 - 2√k
.
.
.

(see if you get k = 25/4)

Answer 2

why do you have the square root of x multiplied by 2 on both sides?

Answer 3

isn't the integral of 1/√x equal to 2√x ??

(differentiate 2√x, what do you get?)

How did you get your answer of 2 from the first part if you didn't have that integral?