Calculating area

Given equations : ${x=17cos^{3}t}$ and $\large{y=5sin^{3}t}$ are parametric equations of the curve:

${ \left( \frac { { x }^{ 2 } }{ { a }^{ 2 } } \right) }^{ \frac { 1 }{ 3 } }+{ \left( \frac { { y }^{ 2 } }{ { b }^{ 2 } } \right) }^{ \frac { 1 }{ 3 } }=1$

$\therefore Area \ = \ 4 \ (area \ in \ 1st \ quadrant)$

$\Rightarrow Area \ = \ 4\int _{ \frac { \pi }{ 2 } }^{ 0 }{ (5{ sin }^{ 3 }t)(-3\times 17{ cos }^{ 2 }t.sint) } dt$

$= \ 12\times 17\times 5\int _{ 0 }^{ \frac { \pi }{ 2 } }{ { sin }^{ 4 }t.{ cos }^{ 2 }t } dt$

On solving further we get:

$=\quad 1020.\frac { 3.1.1 }{ 6.4.2 } .\frac { \pi }{ 2 } =\quad \large{\boxed{\frac { 255\pi }{ 8 }}}$

$\Rightarrow a\quad +\quad b\quad =\quad 255\quad +\quad 6\quad =\quad \boxed{263}$