Chapter 12.7, Problem 4P

Use equation (7.6) to show that ${\displaystyle {\int }_{-1}^1{P}_l}(x)P_{l-1}^{\prime }(x)dx=0.$ Hint: What is the degree of $P_{l-1}^{\prime }(x)?$ Also show that ${\displaystyle {\int }_{-1}^1{P}_l^{\prime }}(x)P_{l+1}(x)dx=0$.