Home
Class 12
MATHS
If the curve y=a x^(1/2)+b x passes thro...

If the curve `y=a x^(1/2)+b x` passes through the point `(1,2)` and lies above the x-axis for `0lt=xlt=9` and the area enclosed by the curve, the x-axis, and the line `x=4` is `8` sq. units, then (a)`a=1` (b) `b=1` `a=3` (d) `b=-1`

A

`a=1`

B

`b=1`

C

`a=3`

D

`b=-1`

Text Solution

Verified by Experts

The correct Answer is:
C, D
Since the curve `y=ax^(1//2)+bx` passes through the point (1,2)
`therefore" "2=a+b" (1)"`
By observation the curve also passes through (0,0). Therefore, the area enclosed by the curve, x-axis and x=4 is given by
`A=overset(4)underset(0)int(ax^(1//2)+bx)dx=8 or (2a)/(3)xx8+(b)/(2)xx16=8`
`or (2a)/(3)+b=1." (2)"`
Solving (1) and (2), we get a =3, b=-1.
Promotional Banner

Topper's Solved these Questions

  • AREA

    CENGAGE ENGLISH|Exercise Linkded Comprehension Type|21 Videos

  • AREA

    CENGAGE ENGLISH|Exercise Matrix Match Type|5 Videos

  • AREA

    CENGAGE ENGLISH|Exercise Exercises - Single Correct Answer Type|40 Videos

  • APPLICATIONS OF DERIVATIVES

    CENGAGE ENGLISH|Exercise Comprehension Type|5 Videos

  • BINOMIAL THEOREM

    CENGAGE ENGLISH|Exercise Matrix|4 Videos

Similar Questions

Explore conceptually related problems

Draw the rough sketch of y^2+1=x ,\ xlt=2. Find the area enclosed by the curve and the line x=2.

Find the area bounded by the curve y=4x-x^2 , the x-axis and the ordinates x=1 and x=3 .

Find the area enclosed between the curve y = x^(2) , the axis and the ordinates x = 1 and x=2 .

Make a rough sketch of the graph of the function y=4-x^2,\ 0lt=xlt=2 and determine the area enclosed by the curve, the x-axis and the lines x=0\ a n d\ x=2.

Find the area enclosed between curve y = x^(2)+2 , x-axis, x = 1 and x = 2 .

Draw a rough sketch of the curve x^2 + y =9 and find the area enclosed by the curve, the x-axis and the lines x + 1 = 0 and x-2 = 0.

The area enclosed by the curve y=x^5 , the x-axis and the ordinates x=-1,x=1 is (A) 0 (B) 1/6 (C) 1/3 (D) none of these

The area enclosed between the curves y=ax^(2) and x=ay^(2)(a gt 0) is 1 sq.unit. Then a =

Show that the area enclosed between the curves y = x and y=x^(3) is (1)/(2) sq unit.

Sketch the graph of y=sqrt(x)+1 "in"[0,4] and determine the area of the region enclosed by the curve, the axis of X and the lines x=0,x=4 .