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General Solution - Calculus - Solved Exam, Exams of Calculus

Institute of Mathematics and ApplicationsCalculus

Calculus is most common subject I know so far. This is one of past exam papers you can find in my uploads. Key points of the exam are: General Solution, Converges, Facts, Diverges, General Solution, Differential Equation, Integrals, Region Bounded, Integral, Volume

Typology: Exams

2012/2013

Uploaded on 03/16/2013

saroj
saroj 🇮🇳

4.5

(2)

151 documents

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1. (8 points) Find the general solution to the following differential equation: (Do not use table of integrals for this problem.) 8" dy = Say7dr . 2. z dy = 5x ax pa dy= [5xe"" dx yo Ay x [one F* do io hoy ( see ax, subshhce w=-3x, duo = —6x4% . ~3Xx aye _ 7 Ww — -Se 4C=u-Se +c: (sxe™® dx = Efe Ao = “Ze eo § -Lle -E ~ 3x Cc. x | _. J 6 < ‘ J for*— C 2. (10 points) Consider the region bounded by y = Inz, the a-axis and the line x = 2. Write (but do not evaluate) an integral to find the volume of the solid obtained by rotating the region about (a) the z-axis Volume. ot chee 2 Try? Ax = 7 (lr x) Ax : 2 Volume of Solid = fap (by xJ dx oO (b) the line z = —1 Ih. Volume of chee = (Tey My OY puk 2 aT =(miat— M4) by =f [2 x =(qn—- Wee) ) Ay - fe Volume t-selid = [r(r-tre) dy 0