Any calculus whiz's out there that can help me?!?

Question

How do I answer this?

Find the region in the first quadrant within the following cardioid.

r=1+cost

t= THETA I can'f rind a theta symbol on my keyboard

Answer 1

region ??

Do you mean you want the area inside the cartioid ??

theta is in radians ??    r = 1 + Cos(t)

Ask the question again, better stated.

Answer 2

int over [0,π/2] of [1/2] r² dt..the integration is trivial if you remember your trig identities....about 4.35

Answer 3

r = 1 + cosθ

Area in the first quadrant

= ∫(θ=0 to π/2) (1/2) r dθ

= (1/2) ∫(θ=0 to π/2) (1 + cosθ) dθ

= (1/2) [θ + sinθ] (θ=0 to π/2)

= (1/2) (π/2 + 1)

= π/4 + 1/2.

You can copy paste the following symbols in a word file or frontpage and save for future use in YA by copy pasting from the saved file.

α β γ δ θ φ √ ± ° ∫ ∞ ≤ ≥ ≠ ∪ ∩ Δ Φ ω Ω π μ ε ≥ ≤ ≦ ≧ ∈ λ x² ρ → ∠ Σ ² σ ∂