\(\displaystyle \int_1^\infty 4x^{-4}\,dx\)
\(\dfrac{4}{3}\)
\(\displaystyle \int_1^\infty 2x^{-1 / 5}\,dx\)
No solution.
\(\displaystyle \int_{-\infty}^\infty \dfrac{4}{36 + x^2}\,dx\)
\(\dfrac{2\pi}{3}\)
\(\displaystyle \int_0^{e^2} \ln x^3\,dx\)
\(3e^2\)
\(\displaystyle \int_3^{9} \dfrac{1}{\sqrt{x^2 - 9}}\,dx\)
\(\ln(3 + 2\sqrt{2})\)
Conclude by giving your students these challenges:
- Gambling at Monte Carlo by NRICH
- Rati-o by NRICH
- Percent Shaded
Place all the digit cards to make all four equations simultaneously true.
What Two ...? by NRICH: Let students know they'll need a calculator to solve this problem.