MATH 172 Midterm: MATH 172 TAMU 172-Spring 18 Exam 2 Solutions
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Z (a) 3z tan2 sec d (b) (c) (d) (e) Solution: e use the trigonometric substitution x = 3. The general partial fraction decomposition of is of the form (a) (b) (c) (d) Solution: d because x4 1 = (x2 1)(x2 + 1) = (x 1)(x + 1)(x2 + 1), we see that the denominator has two distinct linear factors and one irreducible quadratic factor. 1 e (d) e (c) (e) the integral diverges. If we use the trapezoidal rule to approximate. 2 (b) (a) n(cid:20)1 +r4 n(cid:20)r1 n(cid:20)1 + 2r4. Solution: c splitting [1, 3] into n = 6 equal subintervals, we nd width of each subinterval is 3 1. 6 = 2 x0 = 1, x1 = Checking with the formula for the trapezoidal rule, we see that the answer must be c. Find the arc length of the curve between x = 1 and x = 3. y = x3.
