Find the area of the region enclosed in the graph below

Question

Sketch the region enclosed by the graphs of the given functions. Determine whether it is more natural to integrate with respect to x or to y to find the area of the region. Draw a typical approximating rectangle and label the height and width.

y = e^x,  y = x² − 1,  x = −1,  x = 1

Please show all steps and if possible please attach a video going through the whole thing.

Answer 1

Not mentioned in the video answer is the fact that this area could be calculated by using horizontal approximating rectangles (with respect to y), but it would be much more difficult (solving for x in terms of y, and setting up two different integrals.

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