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Grade 10Integral Calculus

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Question image for options 0 1 2 4

Aditya Kartikeya

11 Years agoGrade 10

1 Answer

Jitender Singh

11 Years ago

Ans:
Hello Student,
Please find answer to your question below

$I = \int_{2}^{4}[log_{x}2- \frac{(log_{x}2)^{2}}{log2}]dx$
$I = \int_{2}^{4}[\frac{log2}{logx}- \frac{(log2)^{2}}{log2.(logx)^{2}}]dx$
$I = \int_{2}^{4}[\frac{log2.(logx)}{(logx)^2}- \frac{(log2)}{(logx)^{2}}]dx$
$I = log2\int_{2}^{4}[\frac{(logx)}{(logx)^2}- \frac{1}{(logx)^{2}}]dx$
$I = log2\int_{2}^{4}[\frac{(logx)-1}{(logx)^2}]dx$
$I = log2[\frac{x}{(logx)}]_{2}^{4}$
$I = log2[\frac{4}{(log4)}-\frac{2}{log2}]$
$I = log2[\frac{4}{2log2}-\frac{2}{log2}]$
$I = log2[\frac{2}{log2}-\frac{2}{log2}]$
$I = 0$
Option (1) is correct.

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