Evaluate the integral.

Evaluate the integral

∫8
.......(X^-8/3) dx
1

I need help please! :(
10 points to the best answer :)

p.s. The dots are not really there, it wouldn't let me put a space there.

hi
when an integral contains limits, this wil be called definite integral

as i don't have integral symbol i ve used In
the formula is In x^n dx = x^(n+1)/(n+1)

so In x^-8/3 dx = x^-5/3 / 5/3 = 3/5 x^-5/3
Applying the limits
ans = upper limit - lower limit
= 3/5 [8^-5/3 - 1^-5/3]
= 3/5 [ 2^-5 - 1]
= 3/5 [ 1/32 - 1]
= 3/5 [-31/32]
=- 93/ 160

integral of x^a = x^(a+1) / (a+1)

-8/3 +1 =-5/3, so the indefinite integral is

(-3/5) (x^-5/3) (+C)

evaluate that between the given limits is 93/160 (or about 0.58)