5.12 Integral test

Integral test


Note *The integral test states the following:
If f(x)=anf(x)=a_n and f(x)f(x) is a continuous, positive decreasing function from [i,][i,\infty], then we can say that:
1. If if(x)dx\int_{i}^{\infty}f(x)dx is convergent, then the series n=ian\sum_{n=i}^{\infty}a_n is also convergent.
2. If if(x)dx\int_{i}^{\infty}f(x)dx is divergent, then the series n=ian\sum_{n=i}^{\infty}a_n is also divergent.
  • 2.
    P Series versus Integral test
    Use the integral test instead of the p-series test to show that the series converge or diverge.
  • 3.
    Convergence/Divergence of Integral Test
    Determine whether the following series converge or diverge using the integral test.
Teacher pug

Integral test

Don't just watch, practice makes perfect.

We have over 510 practice questions in Calculus 2 for you to master.