The area bounded by the curve y = f(x), x-axis, and the ordinates x =

1.	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) isA. (x – 1) cos (3x + 4)B. sin (3x + 4)C. sin (3x + 4) +3 (x – 1) cos (3x + 4)D. None of these
Answer» Correct answer is C. So, the area enclosed from x = 1 to x = x (say) is (x – 1) sin (3x + 4) ⇒ A = ∫f(x) dx = F(x) = (x – 1) sin (3x + 4) ⇒ f(x) = F’(x) = sin (3x + 4) + 3(x – 1) cos (3x + 4) (Using u-v rule of differentiation)

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) isA. (x – 1) cos (3x + 4)B. sin (3x + 4)C. sin (3x + 4) +3 (x – 1) cos (3x + 4)D. None of these

Answer»

Correct answer is C.

So, the area enclosed from x = 1 to x = x (say) is (x – 1) sin (3x + 4)

⇒ A = ∫f(x) dx = F(x) = (x – 1) sin (3x + 4)

⇒ f(x) = F’(x) = sin (3x + 4) + 3(x – 1) cos (3x + 4)

(Using u-v rule of differentiation)