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# Areas between curves

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### Areas between curves

1. 1. Exploring areas between curves<br />Task Three<br />
2. 2. THE PROBLEM<br />Find the area bounded by π¦=π₯2+1Β and π¦=βπ₯2+2π₯+1.<br />STEP 1: Graph the equations.<br />Β <br />
3. 3. THE PROBLEM<br />Find the area bounded by π¦=π₯2+1Β and π¦=βπ₯2+2π₯+1.<br />STEP 1: Graph the equations.<br />Β <br />
4. 4. THE PROBLEM<br />Find the area bounded by π¦=π₯2+1Β and π¦=βπ₯2+2π₯+1.<br />STEP 2: Find the intersections to determine the x values which bound the region of the unknown area.<br />Β <br />(1, 2)<br />(0, 1)<br />
5. 5. THE PROBLEM<br />Find the area bounded by π¦=π₯2+1Β and π¦=βπ₯2+2π₯+1.<br />STEP 3: Use logic to determine the best way to get the area.<br />Β <br />(1, 2)<br />(0, 1)<br />Area of Yellow = <br />Area of Blue β Area of Purple<br />within 0β€π₯β€1<br />Β <br />
6. 6. THE PROBLEM<br />Find the area bounded by π¦=π₯2+1Β and π¦=βπ₯2+2π₯+1.<br />STEP 4: SOLVE!<br />Β <br />
7. 7. THE SPECIAL PROPERTY<br />Find the area bounded by π¦=π₯2+1Β and π¦=βπ₯2+2π₯+1.<br />ππππΒ±ππππ=ππππππΒ±ππππππ<br />Area = (Area of Blue β Area of Purple)<br />Area =ππππ₯ππ₯βππππ₯ππ₯<br />Area =ππππ₯Β±ππ₯ππ₯<br />Area=ππ((βπ₯2+2π₯+1)Β βΒ (π₯2+1))ππ₯<br />Area=Β ππ(β2π₯2+2π₯)ππ₯<br />Β <br />
8. 8. THE SPECIAL PROPERTY<br />Find the area bounded by π¦=π₯2+1Β and π¦=βπ₯2+2π₯+1.<br />*CHECK IF ANSWERS ARE CONSISTENT.<br />Area=Β ππ(β2π₯2+2π₯)ππ₯<br />Β <br />