MAT187H1 Midterm: MAT187H1_20151_621426683531mat187-test1
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Make sure you have all of them: you can use pages 12 14 for rough work or to complete a question (mark clearly). No explanation is necessary. (10 marks: consider the solid of revolution generated by revolving the region between two functions f (x) 6 g(x) for x [a, b] around the x axis. Then its volume is given by (circle one choice) (a) z b (b) z b a a (cid:0)g(x) f (x)(cid:1) dx. 2 x(cid:0)g(x) f (x)(cid:1) dx a (c) z b (d) z b a dx. 0 sin83 x cos83 x dx and make a substitution to obtain. 0 sin83 x cos83 x dx = z b a f (u) du. The substitution is u = a : on the integral of question 2, the integrand becomes f (u) , a radioactive material decayed by 10% in 50 years.
