tailieunhanh - Advanced Mathematical Methods for Scientists and Engineers Episode 1 Part 5

Tham khảo tài liệu 'advanced mathematical methods for scientists and engineers episode 1 part 5', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Exercises The Indefinite Integral Exercise mathematica calculus integral Evaluate f 2x 3 10 dx. Hint Solution Exercise mathematica calculus integral Evaluate f lnX dx. Hint Solution Exercise mathematica calculus integral Evaluate x x2 3 dx. Hint Solution Exercise mathematica calculus integral Evaluate f coHX dx. sin x Hint Solution Exercise mathematica calculus integral Evaluate i x dx. x3-5 Hint Solution The Definite Integral Exercise mathematica calculus integral Use the result f x dx lim f xn Ax N rx a n 0 134 where Ax bf and xn a nAx to show that I x dx -. Jo 2 Hint Solution Exercise mathematica calculus integral Evaluate the following integral using integration by parts and the Pythagorean identity. J 0 sin2 x dx Hint Solution Exercise mathematica calculus integral Prove that d ff x _ _ . h C d h f x f x - h g x g x . dx Jg x Don t use the limit definition of differentiation use the Fundamental Theorem of Integral Calculus. Hint Solution Exercise mathematica calculus integral Let An be the area between the curves x and xn on the interval 0. 1 . What is limn_ x An Explain this result geometrically. Hint Solution Exercise mathematica calculus integral a. Show that f x f 0 ỉ x - d . o b. From the above identity show that f x f 0 x i0 u x - d . o .