C3 - Differentiation

    • Thread Starter


    I don't know how to begin solving the second part of the following question:

    i. Given that y = (x + 1)\sqrt{2x - 1} show that \frac{dy}{dx} can be written in the form:

    \displaystyle \frac{kx}{\sqrt{2x - 1}} and state the value of k.

    (This part is fine and I got k = 3)

    ii. Hence evaluate

    \displaystyle \int_1^5\frac{x}{\sqrt{2x - 1}}\ dx

    I do not know how to begin this part. This question is from a differentiation section of the textbook I'm using and so far I have learned only the chain and product rules and do not know how to integrate this so I assume that I am expected to solve this from the first part of the question. If someone could point me in the right direction I would appreciate it.

    Remember that integration reverses differentiation.
    • Thread Starter

    (Original post by Classical Liberal)
    Remember that integration reverses differentiation.
    \displaystyle \int_1^5\frac{x}{\sqrt{2x - 1}}\ dx

    = \displaystyle \frac{1}{3}((5 + 1)\sqrt{2(5) - 1} - (1 + 1)\sqrt{2(1) - 1}) = \frac{16}{3}
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