JEE Main · 2013 · 07 Apr 2013 · Offline · Definite Integrals

At present, a firm is manufacturing 2000 items. It is estimated that the rate of change of production

P

w.r.t. additional number of workers

x

is given by

\frac{d P}{d x} = 100 - 12 x

. If the firm employs 25 more workers, then the new level of production of items is

Answer: (B)

Solution

The extra output is the integral of the rate over the new workers, from

x = 0

25

P - 2000 = \int_{0}^{25} (100 - 12 x) d x = [100 x - 8 x^{3/2}]_{0}^{25} = 100 (25) - 8 (125) = 2500 - 1000 = 1500

. So the new level of production is

P = 3500

items.

JEE Main · 2013 · 07 Apr 2013 · Offline · Single correct option

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