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approximate value of the area of the region y=4x^(2),y=e^(x)

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Answer to a math question approximate value of the area of the region y=4x^(2),y=e^(x)

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Ali

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92 Answers

Step-by-step solution:

1. Set

4x^2 = e^x

to find intersection points.

2. Solve for

using LambertW function:

x = -2\text{LambertW}(-\frac{1}{4})

and

x = -2\text{LambertW}(\frac{1}{4})

.

3. Determine that

4x^2

is on top in the interval between intersection points.

4. Set up the integral

A = \int_{-2\text{LambertW}(-\frac{1}{4})}^{-2\text{LambertW}(\frac{1}{4})} (4x^2 - e^x) \, dx

.

5. Integrate and evaluate at the limits.

6. Numerically calculate the area to get approximately

0.801

square units.

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approximate value of the area of the region y=4x^(2),y=e^(x)

Answer to a math question approximate value of the area of the region y=4x^(2),y=e^(x)

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