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IB Mathematics HL Year I—Unit 8 Quiz Name: Date: Period: 1. The region R is bounded by the curve y = −(x2 − 4x + 3) and the x-axis. Compute the volume of the solid formed by rotating R about the y-axis. 6 - ? 2. The region R is enclosed by the curves y = 1 + ln(x + 1) and y = (x − 1)2 . (a) Sketch the region on the axes below, clearly indicating points of intersection of the two curves. 6 - (b) Set up a definite integral which will compute the volume of the solid obtained by revolving R about the x-axis. (c) Using your graphing calculator or otherwise, compute this volume. 3. Using the substitution u = x2 + 1 or otherwise, compute the Z 1 3 x dx √ definite integral . 2+1 x 0 4. Using an appropriate substitution or otherwise, evaluate the Z trig 2 x dx . indefinite integral x2 + 1