Exercise 11.4: Simple applications of Integral Calculus

EXERCISE 11.4

(1) If f ′(x) = 4x − 5 and f (2) = 1, find f ( x).

(2)  If f ′(x) = 9x2 − 6x and f (0) = −3, find f ( x).

(3) If f ′′(x) = 12x − 6 and f (1) = 30, f ′(1) = 5 find f ( x).

(4) A ball is thrown vertically upward from the ground with an initial velocity of 39.2 m/sec. If the only force considered is that attributed to the acceleration due to gravity, find

(i) how long will it take for the ball to strike the ground?

(ii) the speed with which will it strike the ground? and

(iii) how high the ball will rise?

(5) A wound is healing in such a way that t days since Sunday the area of the wound has been

decreasing at a rate of – 3/(t+2)2 cm2 per day. If on Monday the area of the wound was 2 cm2

(i) What was the area of the wound on Sunday?

(ii) What is the anticipated area of the wound on Thursday if it continues to heal at the same rate?

Answers

Exercise 11.4 (1)2x2+ 5x +3 (2) 3(x3-x2-1) (3) 2x3-3x2+5x+2 (4) (i) 8 seconds (ii) 39.2 m/sec (iii) 78.4 m/sec (5) (i) 2.5 sq.cm (ii) 1.5 sq.cm