Math 162 Worksheet 1 - Chapter 5 Review 1. Use the definition of definite integral (not fundamental theorem of calculus) to evaluate the following integral: (217 - 32 + 5)de Some hints/comments for solving the above problem. You DO NOT have to turn in anything related to the following: . This problem is more difficult than the one we saw in lecture. (Can you spot the key difference?) The main difference is that the INTEGRAND (the function we are integrating) is quadratic, while the example we saw in lecture had a linear integrand. To deal correctly with the quadratic, you have to do the algebra carefully! . We already saw these formulae in lecture: 1=1+1+ ... +1 (n times) = n 1= 1 i=1+2+...+n= n(n + 1) i=1 2 Notice that the last formula is the average of the numbers of n and n + 1. (Can you figure out why this is the case?) You will need the following new formula: 1 = 12 +23 +... +2- n(n+ 1)(2n+ 1) 6