Integral Sinh(x)

Trang chủ » Sinh X Dx » Integral Sinh(x)

Có thể bạn quan tâm

math.com
Home | Teacher | Parents | Glossary | About Us
Homework Help Practice Ask An Expert Calculators & Tools Games Store
Email this page to a friend Email this page to a friend
Resources
· Cool Tools · Formulas & Tables · References · Test Preparation · Study Tips · Wonders of Math
Search
Proof: Integral sinh(x)
(Math | Calculus | Integrals | Table Of | sinh x)
Discussion of (integral) sinh x dx = cosh x + C.

1. Proof

    Strategy: Use definition of sinh.
    sinh x = ex - e-x 2
    (integral) sinh x dx = (integral) ex - ex 2 dx
    = (1/2) (integral) ex dx - (1/2) (integral) ex dx solve left equation = (1/2) ex - (1/2) (integral) ex dx

    set u = - x then we find du = - dx

    substitute du= - dx, u= - x = (1/2) ex + (1/2) (integral) - ex dx = (1/2) ex + (1/2) (integral) eu du

    solve the right integral = (1/2) ex + (1/2) eu + C

    substitute back u= - x = (1/2) ex + (1/2) ex + C

    = ex + ex 2 + C
    which by definition = cosh x + C Q.E.D.

Contact us | Advertising & Sponsorship | Partnership | Link to us © 2000-2023 Math.com. All rights reserved. Legal Notices. Please read our Privacy Policy.

Từ khóa » Sinh X Dx