Question

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

(a) \(\int_c^d y \,dx\)

(b) \(\int_c^d -y \,dx\)

(c) \(\int_c^d x \,dy\)

(d) \(\int_c^d -x \,dy\)

I have been asked this question in examination.

Origin of the question is Quadrature in division Integral Calculus of Engineering Mathematics

Answer 1

Right option is (d) \(\int_c^d -x \,dy\)

To elaborate: The area is present left of y-axis. Area left to y-axis is negative. The area is bounded by y-axis, curve x = f(y), straight lines y=c and y=d. Hence, area is found by integrating the curve with the lines as limits.