Logs and exponential : HELP! (1 Viewer)

excellence1 · Feb 22, 2016

1. How do i integrate ln(x)- does it remain ln(x)

2. Find the volume of the solid formed when the curve y= 2/ root(2x-1) is rotated about the x- axis from x=1 and x=5, giving an exact answer

InteGrand · Feb 22, 2016

excellence1 said:
1. How do i integrate ln(x)- does it remain ln(x)

2. Find the volume of the solid formed when the curve y= 2/ root(2x-1) is rotated about the x- axis from x=1 and x=5, giving an exact answer

$\noindent 1. The integral of $\ln x$ is $x \ln x -x +c$, but you don't need to know how to derive this result unless you do HSC 4U Maths.$

$\noindent 2. The volume is given by$

$\begin{align*}V &= \pi \int_{1} ^{5} y^2 \text{ d}x \\ &= \pi \int _{1} ^{5} \frac{2^2}{2x-1} \text{ d}x \\ &= 2\pi \Big{[} \ln (2x-1)\Big{]}_1 ^5 \\ &= 2\pi \left(\ln 9 - \ln 1\right) \\&= 2\pi \ln 9 \\ &= 4\pi \ln 3 \quad \Big{(}\text{as }\ln 9 = \ln \left(3^2\right) = 2\ln 3\Big{)}.\end{align*}$

excellence1 · Feb 22, 2016

Thanks INTEGRAND!!!!

Logs and exponential : HELP! (1 Viewer)

excellence1

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