Question

What is the formula used to find the area surrounded by the curves in the following diagram?

(a) \(\int_a^b y \,dx\)

(b) \(\int_a^b -y \,dx\)

(c) \(\int_a^b x \,dy\)

(d) \(\int_a^b -x \,dy\)

I have been asked this question in an online interview.

My enquiry is from Quadrature topic in division Integral Calculus of Engineering Mathematics

Answer 1

The correct option is (b) \(\int_a^b -y \,dx\)

To explain I would say: The area is present below the x-axis. Area below the x-axis is negative. The area is bounded by x-axis, curve y = f(x), straight lines x=a and x=b. Hence, area is found by integrating the curve with the lines as limits.