Which statement correctly describes the purpose of solving when computing for the…

MATHEMATICS · Single correct · CBSE · Mathematics · Applications of Integrals · Applications of Integrals

Problem

Which statement correctly describes the purpose of solving

f(x)=g(x)

when computing

\displaystyle\int_a^b\bigl(g(x)-f(x)\bigr)\,dx

for the area enclosed by

y=f(x)

and

y=g(x)

? (a) It reveals which function lies above the other throughout the interval, guaranteeing the integrand

g(x)-f(x)

is non-negative. (b) It determines the

x

-coordinates of the intersection points, which serve as the limits

a

and

b

of the integral. (c) It gives the vertical distance between the curves at every

x

, which is then integrated to find the area. (d) It guarantees that

g(x)-f(x)

is positive on the chosen interval because its sign can change only at those solutions.