Find the area between the curve f(x) = cosx and x= 1 and x= 2

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hala718's profile pic

hala718 | High School Teacher | (Level 1) Educator Emeritus

Posted on

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

               = 0.0173

Then the area btween th curveand x= 1 and x=2= 0.0173 square units.

neela's profile pic

neela | High School Teacher | (Level 3) Valedictorian

Posted on

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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