Question

The region bounded by the x-axis and the part of the graph of y=sinx between x=0 and x=pi is separated into 2 regions by the line x=k. If the area of the region for 0 <(or = to) x <(or = to) k is one-third the area of the region for k <(or = to) x <(or = to) pi, then k=
Answer: pi/3
How do you get this answer?

Answer 1

The line x=k is a vertical line.


To find the area of a region, we need to find the definite integral over the region.
If you can find the area of the region between \(0\le x\le k\) and \(l \le x \le \pi \), you are given the relationship of the two areas.
" If the area of the region for 0 <(or = to) x <(or = to) k is one-third the area of the region for k <(or = to) x <(or = to) pi"
Saying "A is B" is the equivalent of equality: A = B.
So "area of region A is one-third area of region B" is Area of region A = 1/3 Area of region B.

Answer 2

Thank you! :)

Answer 3

Glad to help! :)