Which of the following?

Question

Which of the following gives the value of the area under the curve y=1/(x^2+1) in the first quadrant? 

 

a) pi/4

b) 1

c) pi/2

d) pi

e) diverges 

 

Please show all your work.

Answer 1

It depends of the value of x

 

But area under the curve deals with integral

 

And   ∫ 1⁄ (x² +1) dx =  tan^-1 (x)  (arctan (x))

 

if x = 0 then tan^-1 (0) = 0

 

but if x = 1, then tan^-1 (1) = 45⁰  which is the same as π/4 (pi/4)

 

Note that  sin (x), cos(x)  and tan (x) are all positive in the first quadrant.

 

Hope this helps.