A line tangent to the graph of the function y=f(x) at the point x = a forms an π/3 with y-axis and at x = b an angle π/4 with x-axis then ∫ab f′′(x)dx is
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a
1−13
b
−π12
c
π12
d
3−1
answer is A.
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Detailed Solution
f′(a)=tanπ2−π3=tanπ6=13 and f′(b)=tanπ4=1, so ∫ab f′′(x)dx=f′(b)−f′(a)=1−13.