Problem 41E

Areas of regions

Find the area of the following regions. In each case, graph the relevant functions and show the region in question.

The legion bounded entirely by the curve and the x-axis.

Problem 41E

Find the area of the following regions. In each case, graph the relevant functions and show the region in question.

The region bounded entirely by the curve and the x-axis.

Solution:-

Step 1

The graph of the function is:

The function intersects x-axis at the points when the numerator of the fraction is zero.

Meaning when

To find the roots of this quadratic equation we see

Roots

As we see from the figure the region bounded by and x-axis is from the point .

To find the area of the bounded region, we integrate from .

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Putting the limits in we get the area, we get