Question

The area bounded by x = 1, x = 2, xy = 1 and x-axis is:

• A. log 2
• B. log 3
• C. 2 log 2
• D. 2 log 3

Answer 1

The Correct Option is A

To find the area bounded by the curves x = 1, x = 2, xy = 1, and the x-axis, we need to integrate the function describing the curve xy = 1 between the limits x = 1 and x = 2.

1. The curve xy = 1 can be rewritten as y = 1/x.

2. We set up the definite integral of y from x = 1 to x = 2:

$$\int_{1}^{2}\frac{1}{x}dx$$

3. The antiderivative of 1/x is ln|x|. Therefore, we evaluate the integral:

$$\left[ \ln|x| \right]_{1}^{2} = \ln|2| - \ln|1|$$

4. This simplifies to:

$$\ln 2 - \ln 1$$

5. Since ln(1) = 0, the expression reduces to:

$$\ln 2$$

Thus, the area bounded by the given curves is log 2.