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f(x) = cosx
We know that we can obtin the area by integrting the function.
Let F(x) = integrl f(x)
==> we know that the area is:
A = F(2) - F(1)
Let us integrate f(x):
F(x) = intg cosx dx
= sinx +C
F(2) = sin2 +C
F(1) = sin1+ C
==> A = sin2 - sin1
= 0.0348 - 0.0175
Then the area btween th curveand x= 1 and x=2= 0.0173 square units.
To find the area between f(x) = cosx and x = 1 and x= 2.
We know that the area under f(x) and x axis and between the ordinates x= a and x = b is given by:
F(b) - F(a), where F(x) = Int f(x) dx. a = 1 and x b =- 2.
Therefore F(x) = Int f(x) dx = Int cosxdx = sinx.
Therefore area = F(2) - F(1) = (sin2 )-sin(1) = 0.06783 approximately.
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