Science:Math Exam Resources/Courses/MATH101/April 2018/Question 11 (i)/Statement

Since we all love calculus, lastly we will consider the heart-shaped region ${\textstyle {\mathcal {H}}}$ bounded by

$$\displaystyle x^{2}+\left({\frac {5y}{4}}-{\sqrt {|x|}}\right)^{2}=1\,.$$

The plot of ${\textstyle {\mathcal {H}}}$ is shown below (where the coordinate axes have been deliberately removed).

(i) Determine explicitly the area of ${\textstyle {\mathcal {H}}}$.

Hint: First solve the expression in the equation above for two choices of ${\textstyle y}$ without expanding out the terms in the brackets.