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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
$\int_{a}^{b} f^{''} (x) d x$ is

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1−13

−π12

π12

3−1

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detailed solution

Correct option is A

f′(a)=tan⁡π2−π3=tan⁡π6=13 and f′(b)=tan⁡π4=1, so ∫ab f′′(x)dx=f′(b)−f′(a)=1−13.

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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

Remember concepts with our Masterclasses.

Ready to Test Your Skills?

free study material

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
$\int_{a}^{b} f^{''} (x) d x$ is