Find the area of the region bounded by the curves.

Question

Directions: Find the area of the region bounded by the curves. Use a clean sheet of paper for your solutions and final answers.

questions: https://imgur.com/y718s83

is this correct?- https://imgur.com/pBQulvX

Answer 1

Calculations for 1,2,3,and 5 look spot on. Nice!

I see that instructions ask for sketches which you didn't provide. If you have sketches, and you compare #1 and #4 you will see that the magnitudes of the areas are equal. To simplify #4 you could shift the curve up 4. That integral you've already done in #1. Then at the end recognize that the area is under the x axis so that makes it negative.

Or even easier

Answer 2

Yes, answers are correct, except for #4. Take a look at the following, paying particular attention to problem 4.

desmos.com/calculator/v4ouod5fbf

My recommendation is that when you get to the point where you are evaluating at the final step that you write something like this:

[ ] - [ ], where the antiderivative is evaluated at the upper limit in the first bracket and at the lower limit in the 2nd bracket. I see in your work that you are doing the "subtracting" mentally. If you are confident doing it that way, OK, but doing so has the potential to lead to sign errors.