Determine the area under the curve y=4−x2 from x=−2 to x=2.
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Answer from Sia
Posted about 1 month ago
Solution by Steps
step 1
To find the area under the curve y=4−x2 from x=−2 to x=2, we need to evaluate the definite integral: ∫−22(4−x2)dx
step 2
Calculating the integral, we have: ∫(4−x2)dx=4x−3x3+C
step 3
Now, we evaluate the definite integral from −2 to 2: [4(2)−3(2)3]−[4(−2)−3(−2)3]
step 4
This simplifies to: (8−38)−(−8+38)=(8−38)+(8−38)=16−316=348−316=332
Answer
The area under the curve from x=−2 to x=2 is 332 or approximately 10.667.
Key Concept
The area under a curve can be found using definite integrals.
Explanation
The definite integral calculates the net area between the curve and the x-axis over a specified interval. In this case, it gives the total area under the curve y=4−x2 from $x = -
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