4. ap calculus helpp?

Question

integral from 0 to 1 of x dx / ( x^2 + 1) is = to

Answer 1

Int = 1/2 ln(x^2+1) between (0 and 1) = 1/2(ln 2)

Answer 2

Integral (0 to 1, 1/(x^2 + 1) dx )

This is a known derivative; it's the derivative of arctan.

arctan(x) {evaluated from 0 to 1}

arctan(1) - arctan(0)

arctan(1) is equal to pi/4 (since tan(pi/4) = 1), and arctan(0) is equal to 0 (since tan(0) = 0).

pi/4 - 0

pi/4

EDIT: I read the question incorrectly. The answerer below has it correct.