MATH 1100Y Midterm: MATH1101Y-T2-Solutions (1)
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Legibly, please: if you have a question, ask it, use the back sides of the test sheets for rough work or extra space, you may use a calculator and an aid sheet, do any three (3) of a f. 1 (y + 1)2 dy tet dt: z cos3(x) dx, z sec2(w)ptan(w) dw, z 1. 0: we will use the trig substitution x = 2 sin( ), so dx = 2 cos( ) d and = arcsin(cid:0) x. =z 1 = + c = arcsin(cid:16) x. 2 cos( ) d =z d =z 2 cos( ) 2(cid:17) + c q4 22 sin2( ) p4 cos2( ) 2 cos( ) d d q4(cid:0)1 sin2( )(cid:1) (cid:4: one could just expand the square and integrate away, but we"ll do it using the substi- tution u = y + 1, so du = dy and y 1. 0 u (y + 1)2 dy =z 2. Easier arithmetic this way . u2 du =
