P4:Parametric Integration: Area under a Curve

Find the area enclosed by the parametric curve x = 2sin(t), y = 3cos(t) for 0 ≤ t ≤ π/2.

• 0

• 10

• 5

• 7

Calculate the area under the parametric curve x = 3t^2, y = 2t^3 for t in the interval [1, 2].

• The area under the parametric curve is 25/3 square units

• The area under the parametric curve is 16 square units

• The area under the parametric curve is 94/5 square units

• The area under the parametric curve is 7 square units

Determine the area bounded by the parametric curve x = 4sin(t), y = 3cos(t) for t in the range [0, π].

• 12π

• 2π

• 3π

• 6π

Calculate the area enclosed by the parametric curve x = 2t, y = 3t^2 for t in the range [0, 3].

• 18

• 6

• 24

• 12

Determine the area under the parametric curve x = 3sin(t), y = 4cos(t) for t in the interval [0, π/4].

• 3.535

• 5.678

• 2.718

• 6.283

Find the area bounded by the parametric curve x = 2cos(t), y = 3sin(t) for t in the range [0, π/2].

• 5

• 10

• 2

• 3

Calculate the area under the parametric curve x = 3t^2, y = 2t^3 for t in the interval [0, 1].

• 12

• 5

• 10

• 35/4

Determine the area enclosed by the parametric curve x = 4sin(t), y = 3cos(t) for t in the range [0, 3π/2].

• 9

• 6

• 3

• 12

Find the area enclosed by the parametric curve x = 5sin(t), y = 4cos(t) for t in the range [0, 2π].

• 20π

• 10π

• 15π

• 25π

Calculate the area under the parametric curve x = 2t^2, y = 3t^3 for t in the interval [0, 2].

• The area under the parametric curve is 16 square units

• The area under the parametric curve is 25/3 square units

• The area under the parametric curve is 94/5 square units

• The area under the parametric curve is 7 square units