Improper Integrals with an Infinite Integrand Worksheet with Answer Key

What's on the worksheet

1. Evaluate each integral, or show that it diverges.
   \displaystyle\int_0^{9} \dfrac{1 + \sqrt{x}}{\sqrt{x}}\,dx\displaystyle\int_{-1}^{0} \dfrac{dx}{(x + 1)^3}\displaystyle\int_0^{\pi/2} \dfrac{\cos x}{\sqrt{\sin x}}\,dx\displaystyle\int_0^{1} \dfrac{x}{1 - x^2}\,dx\displaystyle\int_0^{1} \dfrac{\arcsin x}{\sqrt{1 - x^2}}\,dx
2. Evaluate _0^4 x²√(16 - x²)\,dx, or show that it diverges.
3. Evaluate each integral, or show that it diverges.
4. Lily writes _0^π ² x\,dx = π - 0 = 0.
5. Evaluate _-1² x[3]x² - 1\,dx, or show that it diverges.
6. Each integral below is improper at a finite point.