L24 Math 132 Lecture 20: Lecture 20

Problem #5: Find an integral which represents the volume of the solid obtained by rotating the region enclosed by the curves y=x2 and y = 4x + 21 about the x-axis. π [(4x+ 21 )2-4] dr π(x2-4x-21)2 dr π(4x+ 21-x2)2 dr (A) (B) | (C) (E) | (F) | (G) | (II) | π[Y-(4x + 21)2] dr π(x2-4x-21)2 dr π(4x +21-x2)2 dr π[(4x + 21 )2-x4ldr

3. Find a potential function for F(x, y, z)-〈e* cosy + yz,xz-ez sin y, xy. Use it to evaluate (ez cos y + y z) dx + (x z-e* sin y) dy + x y dz where C is any curve froin (0, 0, 0) to (0, π, π-i ) .

4. Use Green's Theorem to evaluate 「 F-dr, if F(x,y)- and C consists of the arc of the curve y= sin x from (0, 0) to (π, 0)and the line segment from ( π , 0) to (0,0).