Let F(x)=\int^{x^2+ \pi/6}_{x}2cos^2 tdt for all x \in \mathbb{R} and f:[0,1/2]\to[0, \infty) be a continuous function.For a \in[0,1/2],\text{if} F'(a)+2 is the area of the region boundary by x=0,y=0,y=f(x)\text{and}x=0\text{then}f(0) is [JEE Adv 2015 P1]

Application of Integration

Section: Mathematics

Question : 18 of 28

Marks: +1, -0

Let F(x)=

x2+

∫

2cos2tdt for all x∈ℝ and f:[0,

]→[0,∞) be a continuous function.For a∈[0,

],if‌F′(a)+2 is the area of the region boundary by x=0,y=0,y=f(x)‌and‌x=0‌then‌f(0) is

[JEE Adv 2015 P1]

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