Integral Calculus
Tangent to integral-defined curve; x-intercept
MMTS_Full_Test_10
Grade 12
Question:
The intercepts on the x-axis made by tangents to the curve $y=\displaystyle\int_0^x|t|\,dt$, $x\in\mathbb{R}$, which are parallel to $y=2x$, are equal to
(A) $\pm3$
(B) $\pm4$
(C) $\pm1$
(D) $\pm2$
Step-by-Step Solution
Key Concept: $dy/dx=|x|=2 \Rightarrow x=\pm2$. At $x=2$: $y=2$; at $x=-2$: $y=\int_0^{-2}|t|dt=-x^2/2|_{x=-2}=-2$.
x-intercepts $=\pm1$.
Correct Answer: (C) $\pm1$