The area of the region bounded by the curve x | vedclass

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Question

(A) The area $A$ of the region bounded by the curve $y = f(x)$,the $x$-axis,and the lines $x = a$ and $x = b$ is given by the formula:$A = \int_{a}^{b

Vedclass · Accepted Answer

$4 \log 3$

Vedclass · Answer

(A) The area $A$ of the region bounded by the curve $y = f(x)$,the $x$-axis,and the lines $x = a$ and $x = b$ is given by the formula:$A = \int_{a}^{b} |f(x)| \, dx$Given the curve $xy = 4$,we have $y = \frac{4}{x}$.The region is bounded by $x = 1$ and $x = 3$.Therefore,the area $A$ is:$A = \int_{1}^{3} \frac{4}{x} \, dx$$A = 4 \int_{1}^{3} \frac{1}{x} \, dx$$A = 4 [\ln |x|]_{1}^{3}$$A = 4 (\ln 3 - \ln 1)$Since $\ln 1 = 0$,we get:$A = 4 \ln 3$Thus,the area is $4 \log 3$ sq. units.

The area of the region bounded by the curve $xy = 4$,$x = 1$,and $x = 3$ is . . . . . . sq. units.

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