The integrand does not behave as 1/[x^(1/3)*x^(1/2)]. Even if it did, 1/x^(1/6) becomes infinitely large as x approaches zero. You're probably thinking of the behavior of a p series, where n is growing infinitely large.1. The problem statement, all variables and given/known data
the integral from 0 to 1 given:
1 / [ (x^1/3)(x^2+2x)^1/2 ] dx
plz explain,, thank you!
3. The attempt at a solution
At 0 the integrand behaves as 1/x^1/3*x^1/2 = 1/x^1/6 which is convergent as the exponent is <1
Substitute WHAT into the integral?could maybe do it 2 ways based on the integral 1->inf of 1/x^n converging iff n>1
2 ways potentially
substitute straight into your integral, changing integration from 0to1 to 1 to infinty, and then use some comparison theorems
Lanedance, I'm not following you here.or substitute into the integral 1->inf of 1/x^n which will change it to 0 to 1, should give you a condition based on n for this integral to converge
i'm thinking it probably does converge at this stage