Find the area enclosed by r = sin 2θ for .

Question

Find the area enclosed by r = sin 2θ for  .Type your answer in the space below and give 3 decimal places. If your answer is less than 1, place a leading "0" before the decimal point 

My answer: 0.392

Answer 1

Area = (1/2)∫_{(from 0 to π/2)} r²dθ = (1/2)∫_{(from 0 to π/2)} sin²(2θ)dθ = (1/2)∫_{(from 0 to π/2)} (1 - cos(4θ))/2 dθ =

(1/4) [θ - (1/4)sin(4θ)]_{(from 0 to π/2)} = π/8 ≈ 0.393 (using the "pi" key on the calculator)