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​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 .

​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-
 
ba ( INTEGRAL WITH LOWER LIMIT a AND UPPER LIMIT b)
 
ba f ‘ ( x ) f  ( x) dx .
 
 

Grade:Select Grade

1 Answers

Jitender Singh IIT Delhi
askIITians Faculty 158 Points
7 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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