Precalculus : Introductory Calculus

Study concepts, example questions & explanations for Precalculus

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Example Questions

Example Question #1 : Area Under A Curve

Approximate the area under the curve given by   on the interval  using right endpoints.

Possible Answers:

Correct answer:

Explanation:

In order to approximate the area under a curve using rectangles, one must take the sum of the areas of discrete rectangles under the curve. Taking the height of each rectangle as the function evaluated at the right endpoint, we obtain the following rectangle areas:

The sum of the individual rectangles yields an overall area approximation of 225.

Example Question #1 : Find The Area Using Limits

What is the area under the curve of the function

from  to .

Possible Answers:

Correct answer:

Explanation:

The area under the curve of the function  is the definite integral from  to .

Remember when integrating, we will increase the exponent by one and then divide the whole term by the value of the new exponent.

From here, we find the difference between the function values of the boundaries.

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