MATH 113 Midterm: MATH 113 BYU KeyW2006
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0 sin x dx : r ln x dx , r /2, r tan x sec2 x dx = x ln x x + c. 2 sec2 x + c: the taylor series for e2x, centered at 0, is 1 + 2x + (2x)2. 2nxn n! dx can be integrated using the trigonometric substitution x = 2 tan x2. X2 + 4: z, the de nite integralr 3 by revolving the curve y = 0 2 x x2 + 1 dx represents the volume of the solid of revolution generated. , x [ 0 , 3 ], about the y-axis. Use the following chart to show your choices for problems 7 13. Only this chart will be graded on these problems. (e) (e) (a) (a) (a) (a) (b) (cid:4) (d) 2 (1 + sin x)p1 + cos2 x dx. (1 + sin x)p1 + sin2 x dx. 2 sin xp1 + sin2 x dx (d) z (f) z 2 .
