Homework Sourse1 Which of the following integrals represents the length of
1) Which of the following integrals represents the length of the curve y=2^x , 0<=x<=3 ?
a. integral from 0 to 3 of sqrt(1+ 2^x) dx
b. integral from 0 to 3 of sqrt (1+ 2^2x) dx
c. integral from 0 to 3 of sqrt (1+ ((ln2)^2)2^2)dx
d. integral from 0 to 3 of sqrt (1+ (2(ln2)^2)2^x)dx
e. integral from 0 to 3 of sqrt (1+ ((ln2)^2)2^x)dx
f. integral from 0 to 3 of sqrt (1+ ((ln2)^2)2^2x)dx
MUST SHOW WORK TO GET POINTS (so I can know how you solved the problem thank you)
a. integral from 0 to 3 of sqrt(1+ 2^x) dx
b. integral from 0 to 3 of sqrt (1+ 2^2x) dx
c. integral from 0 to 3 of sqrt (1+ ((ln2)^2)2^2)dx
d. integral from 0 to 3 of sqrt (1+ (2(ln2)^2)2^x)dx
e. integral from 0 to 3 of sqrt (1+ ((ln2)^2)2^x)dx
f. integral from 0 to 3 of sqrt (1+ ((ln2)^2)2^2x)dx
MUST SHOW WORK TO GET POINTS (so I can know how you solved the problem thank you)
Solution
y = 2x
lny = x ln2
1/y dy = ln2dx
dy = 2x ln2 dx
now length of any small diiferential point with lengths dx and dy = sqrt(dx2 + dy2)
total length = integral sqrt(dx2 +( 2x ln2 dx)2 ) = integral sqrt(1+(2x ln2)2) dx
ans = f. integral from 0 to 3 of sqrt (1+ ((ln2)^2)2^2x)dx
