Integral Calculus
Area Between Curves
MMTS_Full_Test_17
Grade 12
Question:
Let $S$ be the region bounded by the curves $y=x^3$ and $y^2=x$. The curve $y=2|x|$ divides $S$ into two regions of areas $R_1$ and $R_2$. If $\max\{R_1,R_2\}=R_2$, then $\dfrac{R_2}{R_1}=$
Step-by-Step Solution
Key Concept: Find area of S; then subtract area with y=2|x|
Total area $S=\int_0^1(\sqrt{x}-x^3)dx=\frac{2}{3}-\frac{1}{4}=\frac{5}{12}$. $R_1=\frac{5}{12}\cdot\frac{1}{20}$... $R_2/R_1=19$.
Correct Answer: 19