Find the area bounded by the given curves.
\[
y=3 x^{2} \text { and } y=48
\]
square units

Answer

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Answer

Final Answer: \(\boxed{256}\)

Steps

Step 1 ：First, we need to find the points of intersection by setting the two functions equal to each other and solving for x. This gives us \(3x^2 = 48\), which simplifies to \(x = \pm 4\).

Step 2 ：Next, we integrate the absolute difference of the two functions over the interval from -4 to 4. The area is always positive, so we take the absolute value of the difference.

Step 3 ：The integral of the absolute difference of the functions from -4 to 4 is \( \int_{-4}^{4} |48 - 3x^2| dx \).

Step 4 ：Evaluating this integral gives us an area of 256 square units.

Step 5 ：Final Answer: \(\boxed{256}\)

Find the area bounded by the given curves.\[y=3 x^{2} \text { and } y=48\]square units

Answer

Popular Problems

Find the area bounded by the given curves.
\[
y=3 x^{2} \text { and } y=48
\]
square units