Improper Integrals Worksheet with Answer Key

What's on the worksheet

1. Evaluate each improper integral, or show that it diverges.
   \displaystyle\int_8^{\infty} x^{-4/3}\,dx\displaystyle\int_2^{\infty} e^{6 - 3x}\,dx\displaystyle\int_{-\infty}^{-1} \dfrac{dx}{x^2}\displaystyle\int_3^{\infty} \dfrac{dx}{x - 2}\displaystyle\int_0^{\infty} \dfrac{dx}{(x + 3)^3}
2. Evaluate _-∞^∞ e²xe^4x + 4\,dx, or show that it diverges.
3. Evaluate _1^∞ dxx(x + 3)².
4. Evaluate _0^∞ e^-3x(2x)\,dx.
5. Decide whether each integral converges or diverges.
6. Isabel models the power of a fading radio burst picked up by a ground station as $P