Explain why the improper integral converges

MATHEMATICS · Subjective · AP · Calculus BC · Integration and Accumulation of Change · Integration and Accumulation of Change

Problem

Explain why the improper integral ∫1∞1x2 dx\displaystyle \int_{1}^{\infty} \frac{1}{x^{2}}\,dx converges, whereas ∫1∞1x dx\displaystyle \int_{1}^{\infty} \frac{1}{x}\,dx diverges.

Related theory

Browse the problem library