Question

What is the area of a cardiod y = a(1+cosθ).

(a) \(\frac{3πa^2}{2} \)

(b) \(3πa^2 \)

(c) \(\frac{3πa^2}{4} \)

(d) \(\frac{3πa^2}{8} \)

I got this question in an online quiz.

I'm obligated to ask this question of Surface Integrals topic in division Vector Integral Calculus of Engineering Mathematics

Answer 1

Right choice is (a) \(\frac{3πa^2}{2} \)

The explanation is: θ : 0 to π

r : 0 to a(1+cosθ)

\(\frac{Area}{2} = \int_0^π \int_0^{a(1+cosθ)}rdrdθ \)

\(= \frac{3πa^2}{4} \)

Total area = \( 2* \frac{3πa^2}{4} \)

\(\frac{3πa^2}{2} \).