2 Questions here! (I'm not exactly sure if it's allowed, but I want to avoid posting too many threads) 1. The problem statement, all variables and given/known data 1)Find the following definite integrals by using a trigonometric substitution: d)1/2∫1dx/(√(2x-x2) 2. Relevant equations x=asinu 3. The attempt at a solution From a previous question, I found that the indefinite integral of ∫dx/(√(2x-x2) was arcsin(x-1) + C Using FTC part 2, I got: arcsin(1-1)-arcsin(1/2-1)=arcsin0-arcsin(-1/2)=0- -∏/6=∏/6 The answer the teacher gave me was ∏/2 I'm have no idea where I have made a mistake. 1. The problem statement, all variables and given/known data Find the volumes of the solids generated by revolving the region bounded by the curves y=x+2 and y=x2 about (a) the line x=2 (b) the line y=4 2. Relevant equations Shell:V= 2∏a∫bxhdx Disc: V=∏a∫br22-r12dx 3. The attempt at a solution a) x+2=x2 0=x2-x+2 (-b±√(b2-4ac))/2a=(1±√(1-4(1)(-2))/2(1)=(1±3)/2 x=-1 and x=2 2∏-1∫2x*(x+2-x2)dx 2∏(1/3*x3+x2-1/4x4|-12 2∏(8/3-5/12)= 9∏/2 The correct answer was supposed to be 27∏/2 b) ∏a∫b(4-(x2)2(4-(x+2))2dx ∏a∫b12-9x2+4x-x4dx ∏(12x-3x3+2x[sup2]-1/5x[sup5])|-12 ∏[(24-24+8-32/5)-(-12+3+2+1/5)]= 42∏/5 The answer is supposed to be 108∏/5 Thanks!