Hey there! Sign in to join this conversationNew here? Join for free
    • Thread Starter
    Offline

    1
    ReputationRep:
    a) integrate xsin(2x)

    did this part fine, answer is -1/2xcos(2x) + 1/4sin(2x) +C

    b) given y=0 when x= 1/4pi, solve dy/dx = xsin(2x)cos^2(y)

    I realise I must be missing some trick, should probably have just paid attention in class, any help would be great.
    Offline

    22
    ReputationRep:
    (Original post by jameshegarty)

    b) given y=0 when x= 1/4pi, solve dy/dx = xsin(2x)cos^2(y)
    Separable:

    \displaystyle

\begin{equation*}\frac{\mathrm{d  }y}{\mathrm{d}x} = x\sin x\cos^2 y \Rightarrow \int \frac{1}{\cos^2 y} \, \mathrm{d}y = \int x\sin 2x \,\mathrm{d}x\end{equation*}

    You know how to integrate the RHS from part(a), the LHS is \frac{1}{\cos^2 y} = \sec^2 y which you should know integrates to...?
    Spoiler:
    Show
    What does \tan x differentiate to?
    • Thread Starter
    Offline

    1
    ReputationRep:
    (Original post by Zacken)
    Separable:

    \displaystyle

\begin{equation*}\frac{\mathrm{d  }y}{\mathrm{d}x} = x\sin x\cos^2 y \Rightarrow \int \frac{1}{\cos^2 y} \, \mathrm{d}y = \int x\sin 2x \,\mathrm{d}x\end{equation*}

    You know how to integrate the RHS from part(a), the LHS is \frac{1}{\cos^2 y} = \sec^2 y which you should know integrates to...?
    Spoiler:
    Show
    What does \tan x differentiate to?
    loooooooooool, im a massive idiot. safe
    Offline

    22
    ReputationRep:
    (Original post by jameshegarty)
    loooooooooool, im a massive idiot. safe
    Awesome.
 
 
 
  • See more of what you like on The Student Room

    You can personalise what you see on TSR. Tell us a little about yourself to get started.

  • Poll
    What's your favourite Christmas sweets?
    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

    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
  • See more of what you like on The Student Room

    You can personalise what you see on TSR. Tell us a little about yourself to get started.

  • 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

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