Turn on thread page Beta
    • Thread Starter
    Offline

    2
    ReputationRep:
    The 2 has disappeared in the integration and I am very sad because I don't know why

    I know secxtanx integrated = secx which is why it equals sec^2x but the constant 2 is just gone and I wondered if there was an explanation behind this!



    Someone explain please?
    • Study Helper
    Online

    15
    Study Helper
    (Original post by Crazydavy)
    Someone explain please?
    Try differentiating sec^2 x and see what you get. Use the chain rule.
    Offline

    8
    ReputationRep:
    (Original post by Crazydavy)
    The 2 has disappeared in the integration and I am very sad because I don't know why

    I know secxtanx integrated = secx which is why it equals sec^2x but the constant 2 is just gone and I wondered if there was an explanation behind this!



    Someone explain please?
    AS sec'x=secx\cdot tanx
    your integral form is
    \int f'(x)\cdot f^n(x)\ dx=\frac{f^{n+1}(x)}{n+1}+C
    2\int secx\cdot sec'x\ dx=2\cdot \frac {sec^2x}{2}+C
    • Thread Starter
    Offline

    2
    ReputationRep:
    Thanks you two!!
    Offline

    13
    ReputationRep:
    (Original post by ztibor)
    AS sec'x=secx\cdot tanx
    your integral form is
    \int f'(x)\cdot f^n(x)\ dx=\frac{f^{n+1}(x)}{n+1}+C
    2\int secx\cdot sec'x\ dx=2\cdot \frac {sec^2x}{2}+C
    Shouldn't it be (f(x))^{n+1}

    Because using that notation is like: (for example)
    f(x)=sin(x)
    f^{2}(x)=sin(sin(x))

    :confused:
    Offline

    8
    ReputationRep:
    (Original post by ElMoro)
    Shouldn't it be (f(x))^{n+1}

    Because using that notation is like: (for example)
    f(x)=sin(x)
    f^{2}(x)=sin(sin(x))

    :confused:
    f^n(x) means here [f(x)]^n
    n can be any real (even 1) except 0 and -1
    the nth derivative of f
    f^{(n)}(x)
    or the second derivative
    f^{(2)}(x)=f''(x)
    • PS Helper
    Offline

    14
    PS Helper
    (Original post by ztibor)
    f^n(x) means here [f(x)]^n
    n can be any real (even 1) except 0 and -1
    the nth derivative of f
    f^{(n)}(x)
    or the second derivative
    f^{(2)}(x)=f''(x)
    It's usually a better idea to write (f(x))^n, or f(x)^n if you don't want to use brackets. It's quite ambiguous notation, but when I see f^n(x) (where n > 0) I interpret it to mean \displaystyle ( \underbrace{f \circ f \circ \cdots \circ f}_{n \text{ times}})(x).
 
 
 
Reply
Submit reply
Turn on thread page Beta
Updated: March 15, 2011

University open days

  • University of Buckingham
    Psychology Taster Tutorial Undergraduate
    Fri, 14 Dec '18
  • University of Lincoln
    Mini Open Day at the Brayford Campus Undergraduate
    Wed, 19 Dec '18
  • University of East Anglia
    UEA Mini Open Day Undergraduate
    Fri, 4 Jan '19
Poll
Were you ever put in isolation at school?
Useful resources

Make your revision easier

Maths

Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

Equations

How to use LaTex

Writing equations the easy way

Equations

Best calculators for A level Maths

Tips on which model to get

Student revising

Study habits of A* students

Top tips from students who have already aced their exams

Study Planner

Create your own Study Planner

Never miss a deadline again

Polling station sign

Thinking about a maths degree?

Chat with other maths applicants

Can you help? Study help unanswered threads

Groups associated with this forum:

View associated groups

The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE

Write a reply...
Reply
Hide
Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.