integrate sqrt(4-x^2)?

0 ⤊

integrate sqrt(4-x^2)?

by trigonometric substitution method

2007-06-23 09:04:36 · 4 answers · asked by aoc10010001100 2 in Science & Mathematics ➔ Mathematics

4 answers

put x = 2sinθ then dx = 2cosθ dθ
Hence, int ((4-x^2)^1/2) = int ( (2cosθ)(2cosθ) dθ)
= 4 int(cos^2 θ dθ) = 4/2 (θ + sin2θ / 2) +c
=2θ +sin2θ +c
where c = any constant
hence, integration becomes, =2 arcsin (x/2) +2 (x/2) sqrt (1-x^2 /4) +c
= 2arcsin (x/2) + (x/2) sqrt (4-x^2) +c

2007-06-23 09:19:23 · answer #1 · answered by saeed 2 · 0⤊ 0⤋

= x/2 sqrt(4-x^2) +2arcsin(x/2) + C

2007-06-23 16:20:22 · answer #2 · answered by ironduke8159 7 · 0⤊ 0⤋

integral (sqrt(4-x^2)) = 2arcsin(x/2) + xroot(4-x^2)/2

2007-06-23 16:14:59 · answer #3 · answered by J Z 4 · 0⤊ 1⤋

124

2007-06-23 16:20:13 · answer #4 · answered by Anonymous · 0⤊ 1⤋