Calculate the area under the graph of f(x)=1/(x^2+1) in the first quadrant
a) pi/4
b) pi/2
c) pi
d) infinite
c'mon - this is one of the standard forms -- arctan(x)
I don't understand. what do you mean?
a trig substitution is used when calculating the integral
as oobleck says, it's a standard trick
To calculate the area under the graph of f(x) = 1 / (x^2 + 1) in the first quadrant, we need to integrate the function over the appropriate interval.
In this case, we want to find the area from x = 0 to x = +∞. Since the function extends indefinitely in the positive x direction, the area is technically infinite.
Therefore, the correct answer is (d) infinite.