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SSC Applied Mathematics QUESTION #1321
Question 1
The area enclosed between two curves \(y=f(x)\) and \(y=g(x)\) where \(f(x)\geq g(x)\) on \([a,b]\) is given by:
  • \(\int_a^b[f(x)+g(x)]\,dx\)
  • \(\int_a^b[f(x)-g(x)]\,dx\)✔️
  • \(\int_a^b[f(x)\cdot g(x)]\,dx\)
  • \(\dfrac{1}{2}\int_a^b[f(x)-g(x)]\,dx\)
Correct Answer Explanation
The area between two curves is the integral of the top curve minus the bottom curve: \(A=\int_a^b[f(x)-g(x)]\,dx\) where \(f(x)\geq g(x)\) on \([a,b]\). The limits \(a\) and \(b\) are the \(x\)-coordinates of the intersection points.