For hours, water flows into and out of a storage tank at a rate liters per hour.…

MATHEMATICS · Single correct · A Level · Mathematics · Integration · Integration

Problem

For

0\le t\le 2\pi

hours, water flows into and out of a storage tank at a rate

R(t)=5\cos t-3

liters per hour. Which interval yields the greatest net increase in the amount of water in the tank? (a)

[0,\,\pi]

(b)

[0,\,2\pi]

(c)

[0,\,\tfrac{\pi}{2}]

(d)

[\tfrac{\pi}{2},\,\pi]