The area bounded by the curve y = f(x), x-axis and ordinates... | MATH - AREA BOUNDED BY REGION, VOLUME AND SURFACE AREA OF SOLIDS OF REVOLUTION | SolveeIt | Solveeit

Today, August 18

Question

The area bounded by the curve y = f(x), x-axis and ordinates x = 1 and x = b is (b –1) sin (3b + 4), then f(x) =

A

3(x–1) cos (3x + 4) + sin (3x + 4)

B

(b – 1) sin (3x + 4) + 3 cos (3x + 4)

C

(b – 1) cos (3x + 4) + 3 sin (3x + 4)

D

None of the above

Answer

3(x–1) cos (3x + 4) + sin (3x + 4)

Explanation

Solution

Area bounded by the curve y = f(x), x-axis and x = 1 & x = b is $\int _ { 1 } ^ { b } f ( x ) d x = ( b - 1 ) \sin ( 3 b + 4 )$

On differentiating w.r.t b we get f(2) × 1 = 3(b – 1) cos (3b + 4) + sin (3b + 4)

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