# Why does integration find the area under a curve?

Let us look at the definition of a definite integral below.

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Integration finds the area under a curve because it essentially calculates the accumulation of infinitely small segments or rectangles that approximate the shape of the curve. By summing up these infinitesimal areas, integration provides a precise measurement of the total area enclosed by the curve and the x-axis within specified boundaries. This process is based on the fundamental theorem of calculus, which links differentiation and integration, allowing for the determination of areas, among other applications.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

- How do you find the definite integral for: #(6x+3)dx# for the intervals #[3, 9]#?
- How do you use the Fundamental Theorem of Calculus to evaluate an integral?
- How do you integrate #1/tan(x) dx#?
- Find the indefinite integral. (Note: Solve by the simplest method—not all require integration by parts. Use C for the constant of integration.)?
- What is the integral of #2e^(2x)#?

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