Definite integral

Front

What is a definite integral?

Back

Front

What does the Fundamental Theorem of Calculus state?

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What is the area under the curve y = 3x^2 - 2x from x = 1 to x = 5?

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Front

What does it mean if a definite integral evaluates to zero?

Back

If a definite integral evaluates to zero, it indicates that the areas above and below the x-axis cancel each other out over the interval.

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The integral evaluates to 0, as the function is odd and symmetric about the origin.

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What is the geometric interpretation of a definite integral?

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The geometric interpretation of a definite integral is the net area between the curve of the function and the x-axis over the specified interval.

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What is the difference between definite and indefinite integrals?

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A definite integral has specific limits and results in a numerical value, while an indefinite integral does not have limits and results in a family of functions plus a constant.

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How do you find the area under a curve using definite integrals?

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To find the area under a curve, set up the definite integral of the function over the desired interval and evaluate it.

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What is the significance of the limits of integration in a definite integral?

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The limits of integration define the interval over which the area is calculated and determine the bounds of the integral.