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The slope of the tangent to a curve y=f(...

The slope of the tangent to a curve `y=f(x)` at `(x,f(x))` is `2x+1.` If the curve passes through the point `(1,2)` then the area of the region bounded by the curve, the x-axis and the line `x=1` is (A) `5/6` (B) `6/5` (C) `1/6` (D) `1`

A

`(5)/(6)` sq unit

B

`(6)/(5)` sq unit

C

`(1)/(6)` sq unit

D

6 sq unit

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A
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Knowledge Check

  • The slope of the tangent to a cruve y=f(x) at (x,f(x)0 is 2x+1 .If the curve passes through the point (1,2) then the area of the region bounded by the curve,the x-axis and the lien x=1 is

    A
    `5/6` sq. units
    B
    `6/5` sq.units
    C
    `1/6` sq. units
    D
    `6` sq. units

  • The area of the region bounded by the curve C :y=(x+1)/(x^(2)+1) nad the line y=1 , is

    A
    ml `-(1)/(2)"In"2+(pi)/(4)`
    B
    `"In" 2-(pi)/(4)+1`
    C
    `(1)/(2)"In" 2+(pi)/(4)-1`
    D
    In `2-(pi)/(2)+1`

  • Area bounded by the curve y = sin^(-1)x , the X-axis and the line 2x = 1 is

    A
    `(pi)/(12)+(sqrt(3))/(2)`
    B
    `(pi)/(12)-(sqrt(3))/(2)`
    C
    `(pi)/(12)-1`
    D
    `(pi)/(12)+(sqrt(3))/(2)-1`

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