MIT single variable calculus polar coordinate problem sheet questions

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I'm currently going through MIT's single variable calculus series, so far most the problem sheet questions are similar to the examples in the lecture, however I've just got to the polar coordinates section and I'm finding it difficult to apply what I've learned from the lectures to the problem set. I was wondering if anyone knows any resources I could use to help understand 4H-2 as I'm really at a loss how to solve these types of questions. Any help would be greatly appreciated, thanks.

Problem sheet: https://ocw.mit.edu/courses/mathematics/18-01sc-single-variable-calculus-fall-2010/unit-3-the-definite-integral-and-its-applications/part-a-definition-of-the-definite-integral-and-first-fundamental-theorem/problem-set-6/MIT18_01SC_pset4prb.pdf