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Area between the curves Y=sinx and Y=[sinx]from x=0 to x=2pi is
let f(x) , g(x) be the two functions f(x) = sinx g(x) = [sinx] area bw two curves is {f(x) - g(x)}dx lim from 0 to pi A = {sinx - [sinx]}dx lim from 0 to pi A = sinxdx - [sinx]dx lim 0 to pi A = I1 - I2 ..............................1 I1 = sinxdx lim 0 to pi I1 = -cosx lim 0 to pi I1 = -[cospi-cos0] = 2 I2 = [sinx]dx lim 0 to pi = [sinx]dx lim 0 to pi/2 + [sinx]dx lim pi/2 to pi = 0 + 0 = 0 A = I1 - I2 = 2units
let f(x) , g(x) be the two functions
f(x) = sinx
g(x) = [sinx]
area bw two curves is {f(x) - g(x)}dx lim from 0 to pi
A = {sinx - [sinx]}dx lim from 0 to pi
A = sinxdx - [sinx]dx lim 0 to pi
A = I1 - I2 ..............................1
I1 = sinxdx lim 0 to pi
I1 = -cosx lim 0 to pi
I1 = -[cospi-cos0] = 2
I2 = [sinx]dx lim 0 to pi
= [sinx]dx lim 0 to pi/2 + [sinx]dx lim pi/2 to pi
= 0 + 0 = 0
A = I1 - I2 = 2units
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