MAT136H1 Quiz: MAT136H1 Long Quiz 1 2015 Fall Solutions

• School: UTSG
• Department: Mathematics
• Course: MAT136H1
• Professor: All

Document Summary

1: write the integral cos(x) dx as a limit of riemann sums. Solution: notice that a = 0 and b = 0. Therefore, x = b(cid:0)a n and xi = a + i x = 1: in consequence, n i n. Good luck! n cos(x) dx = lim n!1. 0 i=1 cos(xi) x = lim n!1 cos i=1: what is the average value of f (x) = x cos(x) on the interval [(cid:0)(cid:25); (cid:25)]. Solution: notice that f ((cid:0)x) = (cid:0)x cos((cid:0)x) = (cid:0)x cos(x) = (cid:0)f (x): Thus, (cid:25)(cid:0)(cid:25) x cos(x) dx = 0. (cid:25) x cos(x) dx = 0: (cid:0)(cid:25) favg = 2(cid:25) (cid:0)1 x tan x2 + 1: find dx. Solution: let u = tan (cid:0)1(x), then du = dx. Therefore, (cid:0)1 x tan x2 + 1 dx = u du = u2 u. 2 + c: (cid:0)1(x) tan: find the area of the region bounded by the curves y = 3x and y = 3x2.