Definite Integration Question 389
Question: If a curve $ y=a\sqrt{x}+bx $ passes through the point (1, 2) and the area bounded by the curve, line $ x=4 $ and x-axis is 8 sq. unit, then
[MP PET 2002]
Options:
A) $ a=3,b=-1 $
B) $ a=3,b=1 $
C) $ a=-3,b=1 $
D) $ a=-3,b=-1 $
Show Answer
Answer:
Correct Answer: A
Solution:
Given curve $ y=a\sqrt{x}+bx $ . This curve passes through (1, 2),
$ \therefore 2=a+b $ ……(i) and area bounded by this curve and line $ x=4 $ and x-axis is 8 sq. unit, then $ \int _{0}^{4}{(a\sqrt{x}+bx)}dx=8 $
therefore $ \frac{2a}{3}[{x^{3/2}}]_0^{4}+\frac{b}{2}[x^{2}]_0^{4}=8 $ , $ \frac{2a}{3}.8+8b=8 $
therefore $ 2a+3b=3 $ ……(ii) From equation (i) and (ii), we get $ a=3,b=-1 $ .
BETA
