MAT 21B Midterm: MAT 021B - Term Test 2

• School: UC-Davis
• Department: Mathematics
• Course: MAT 21B
• Professor: All

Document Summary

Chapter 6: applications of definite integrals: 6. 2 volumes using cylindrical shells, 6. 3 arc length, 6. 4 areas of surfaces of revolution, 6. 5 work and fluid forces, 6. 6 moments and centers of mass. Chapter 7: integrals and transcendental functions: 7. 1 the logarithm defined as an integral, 7. 2 exponential change and separable differential equations. Ex: set up an integral for the volume of the solid with. Base: bounded by (cid:1877) = 2(cid:1876)% and (cid:1877) = (cid:1876)% + 9. Cross-sections: perpendicular to x-axis semicircular regions (cid:1848) = ) ((cid:1876)) (cid:1856)(cid:1876) = 0 (9 (cid:1876)%) (cid:1848) = - A solid of revolution is formed by revolving a region in the plane around a line (called the axis of revolution). Or ball: disk method: x- axis, the volume of the resulting solid is given by. If the region under (cid:1877) = (cid:1858)((cid:1876)) for (cid:1853) (cid:1876) (cid:1854) is revolved about the (cid:1848) = @ ((cid:1858)((cid:1876))% (cid:1856)(cid:1876) since = (cid:1870)% = b(cid:1858)((cid:1876))c%