Question

The region r is enclosed by the curves y=4-4x2 and y=0

Answer 1

The region r is enclosed by the curves y₁ = 4 - 4x² and y₂ = 0 is 16/3 or 5.333 square units.

What is an area bounded by the curve?

When the two curves intersect then they bound the region is known as the area bounded by the curve.

The region r is enclosed by the curves y₁ = 4 - 4x² and y₂ = 0

The intersection points will be

       y₁ = y₂

4 - 4x² = 0

        x = ±1

Then the area bounded by the curves will be

$\rm Area = \int _{-1}^1 (y_1- y_2) dx\\\\Area = \int _{-1}^1 (4 - 4x^2) dx\\\\Area = \left [ 4x - \dfrac{4x^3}{3} \right ]_{-1}^1\\\\Area = 4 \left ( 1 + 1 \right ) - \dfrac{4}{3} \left ( 1^3 - (-1)^3 \right )\\\\Area = 8 - \dfrac{8}{3}\\\\Area = \dfrac{16}{3} = 5.333$

More about the area bounded by the curve link is given below.

brainly.com/question/24563834

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