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Grade Select GradeDifferential Calculus

Q. THE TANGENT TO THE GRAPH OF THE FUNCTION- y = f( x ) AT THE POINT WHERE THE ABSCISSA 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

11 Years agoGrade Select Grade

1 Answer

Jitender Singh

Approved Tutor Answer11 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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