The area bounded by the curve xy = c,the x-ax | vedclass

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(A) The area $A$ bounded by the curve $y = f(x)$,the $x$-axis,and the lines $x = a$ and $x = b$ is given by $A = \int_a^b y \, dx$. Given the curve $x

Vedclass · Accepted Answer

$2c \log 2 	ext{ sq. units}$

Vedclass · Answer

(A) The area $A$ bounded by the curve $y = f(x)$,the $x$-axis,and the lines $x = a$ and $x = b$ is given by $A = \int_a^b y \, dx$. Given the curve $xy = c$,we have $y = \frac{c}{x}$. Substituting the limits $x = 1$ and $x = 4$,the area is: $A = \int_1^4 \frac{c}{x} \, dx$ $A = c [\ln |x|]_1^4$ $A = c (\ln 4 - \ln 1)$ Since $\ln 1 = 0$ and $\ln 4 = \ln(2^2) = 2 \ln 2$,we get: $A = c(2 \ln 2) = 2c \ln 2 	ext{ sq. units}$.

The area bounded by the curve $xy = c$,the $x$-axis,and the lines $x = 1$ and $x = 4$ is:

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