Area between three curves involves tangent line Let $R$ be the region enclosed by the $x$-axis, the curve $y=x^{2}$, and the tangent to the curve at $x=a$, where $a>0$. If the area of $R$ is $\frac{2}{3}$, then the value of $a$ is?
Is there any clue for the tangent equation and how's the integral equation will be?
Thanks!

Hints :
tangent is passing through $(a,a^2)$ where its slope would be $\displaystyle{\frac{dy}{dx}|_{x=a}}$
Area of R would be the difference between the region of curve and the region of tangent line enclosed by the x-axis. (from $0$ to $a$)
