Definite Integration Question 329
Question: Let y be the function which passes through (1, 2) having slope $ (2x+1) $ . The area bounded between the curve and x-axis is
[DCE 2005]
Options:
A) 6 sq. unit
B) 5/6 sq. unit
C) 1/6 sq. unit
D) None of these
Show Answer
Answer:
Correct Answer: C
Solution:
$ \frac{dy}{dx}=2x+1 $
therefore $ y=x^{2}+x+c $
therefore $ y=x^{2}+x $ , [ $ \because $ c = 0 by putting x = 1, y = 2)
therefore $ {{( x+\frac{1}{2} )}^{2}}=y+\frac{1}{4} $ , which is a equation of parabola, whose vertices is, $ V( \frac{-1}{2},\frac{-1}{4} ) $
$ \therefore $ Required area $ =. | \int _{-1}^{0}{(x^{2}+x)\ dx} . | $
$ =( \frac{x^{3}}{3}+\frac{x^{2}}{2} ) _{-1}^{0} $
$ . =| \frac{-1}{3}+\frac{1}{2} . |=\frac{1}{6} $ sq. unit.
BETA
