MATH 221 Midterm: MATH 221 KSU f15Test 2

• School: Kansas State University
• Department: Mathematics
• Course: MATH 221
• Professor: All

Document Summary

The point value of each problem is given in the left-hand margin. Z pu2 a2 du = sec 1(|x| a. 2 (cid:16)upa2 u2 + a2 sin 1 u a(cid:17) + c , 2 (cid:16)upu2 a2 a2 ln |u +pu2 a2|(cid:17) + c. Units of force: pounds, newtons; gravitational acceleration: g = 9. 8m/sec2. Hooke"s law for springs: f = kx , where x is the distance stretched from rest position. Moments: for the region between y = f (x) and y = g(x) , with a x b , 2 r b a f (x)2 g(x)2 dx , my = r b a x(f (x) g(x)) dx . |rn(x)| k (n+1)!|x a|n+1 , with k = maxa c x |f (n+1)(c)| . (10) 1. Calculate the length of the curve y = x2 , 0 x 1 . (make use of an appropriate integral on the cover page if necessary. ) page 1 of 5 (10) 2.