M-172Q Midterm: MATH 172 Montana State Exam2
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23 may 2013: integrate. (a) [6] z x ln x dx (b) [6] z x sec2 x dx. 0 x cos x dx: integrate. (a) [6] z tan2 x sec4 x dx (b) [6] z sin3 t cos3 t dt (c) [8] z t sin3 (t2) dt, integrate. (a) [10] z dx. X2 + 6x (b) [10] z e t dt. [hint: let x = t: [15] calculate the work (in joules) required to pump all of the water out of the full hemispherical tank in the gure below; water exits through the spout. Distances are in meters, the density of water is , acceleration due to gravity is g. please specify your coordinate system: [15] use the substitution t = 3 tan to evaluate the following integral. You will nd the identity sin (2 ) = 2 sin cos useful.
