Flashcards

Application of Integrals
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Question

What is the formula for the area of the region bounded by the curve y=f(x)y=f(x), the x-axis, and the lines x=ax=a and x=bx=b?

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Answer

The formula for the area A is given by the definite integral: A=∫aby dx=∫abf(x) dxA = \int_{a}^{b} y \, dx = \int_{a}^{b} f(x) \, dx This is derived by summing the areas of an infinite number of thin vertical strips.

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