Question
Question: The area bounded by the curve y = f(x), x-axis and the ordinates x = 1 and x = b is (b – 1) sin (3b ...
The area bounded by the curve y = f(x), x-axis and the ordinates x = 1 and x = b is (b – 1) sin (3b + 4), then f(x) equals –
A
(x – 1) cos (3x + 4)
B
sin (3x + 4)
C
sin (3x + 4) + 3 (x – 1) cos (3x + 4)
D
None of these
Answer
sin (3x + 4) + 3 (x – 1) cos (3x + 4)
Explanation
Solution
As given 
= (b – 1) sin (3b + 4) Now differentiating with respect to b (using [P-9] from definite integral)
ƒ(2).1 = sin (3b + 4) + 3(b – 1) cos (3b + 4)
\ ƒ(x) = sin(3x + 4) + 3(x – 1) cos (3x + 4)