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

The question was asked in my homework.

The doubt is from Quadrature topic in division Integral Calculus of Engineering Mathematics

Answer 1

Right answer is (c) \(\int_c^d x \,dy\)

Explanation: The area is present right of y-axis. Area right to y-axis is positive. The area is bounded by the 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.