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Differential Calculus> Q. THE TANGENT TO THE GRAPH OF THE FUNCT...

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Q.THE TANGENT TO THE GRAPH OF THE FUNCTION- y = f( x ) AT THE POINT WHERE THEABSCISSA x = a FORMS AN ANGLE OF pi/6 WITH THE X-AXIS AND AT THE POINT x = b AN ANGLE OF pi/4 , THEN FIND THE VALUE OF THE INTEGRAL- b∫a ( INTEGRAL WITH LOWER LIMIT a AND UPPER LIMIT b) b∫a f ‘ ( x ) f ” ( x) dx .

Bharat Makkar , 10 Years ago

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Jitender Singh

Last Activity: 10 Years ago

Ans:
Hello Student,
Please find answer to your question below

$f'(a) = tan(\frac{\pi }{6})$
$f'(a) = \frac{1}{\sqrt{3}}$
$f'(b) = tan(\frac{\pi }{4})$
$f'(b) = 1$
$I = \int_{a}^{b} f'(x)f''(x)dx$
$f'(x) = t$
$f''(x)dx = dt$
$I = \int_{f'(a)}^{f'(b)} tdt$
$I = [\frac{t^2}{2}]_{f'(a)}^{f'(b)}$
$I = [\frac{t^2}{2}]_{1/\sqrt{3}}^{1}$
$I = \frac{1}{3}$

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