Question

Find the exact area bounded by the curve y=cos 3x, the x-axis and the line x=0 and x=π/12?

thanks soo much

Answer 1

Bounded area is `0.2357` sq.unit

Explanation:

Area of the region bounded by the graph of f, the x-axis and the

vertical lines `x=a and x=b` is given by: `A=int_a^b f(x) dx`

Bounded area is `A=int_0^(pi/12) cos (3 x ) dx`

or `A=[ sin (3 x)/3]_0^(pi/12)`

`=1/3[ sin (3 *pi/12)-sin (3 *0) ]`

`=1/3[ sin (pi/4)-sin (0) ]`

`=1/3* 1/sqrt 2 = 1 /(3 sqrt 2) ~~ 0.2357( 4 dp)` [Ans]