Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app

BITSAT 2014

Exam: BITSAT
Year: 2014
Subject: Mathematics
Chapter: Area Under Curves

BITSAT 2014 · Mathematics · Area Under Curves

The area bounded by the x -axis, the curve y=f(x) and the lines...

The area bounded by the

x

-axis, the curve

y=f(x)

and the lines

\mathrm{x}=1,

\mathrm{x}=\mathrm{b}

,

is equal to

\sqrt{\mathrmb^{2}+1}-\sqrt{2}

for all

b > 1,

then

f(x)

is

Options

A $\sqrt{x-1}$
B $\sqrt{x+1}$
C $\sqrt{x^{2}+1}$
D $\frac{x}{\sqrt{1+x^{2}}}$

Correct answer

D. $\frac{x}{\sqrt{1+x^{2}}}$

Step-by-step solution

Given

\int_{1}^{\mathrm{b}} \mathrm{f}(\mathrm{x}) \mathrm{dx}=\sqrt{\mathrmb^{2}+1}-\sqrt{2}

Differentiate with respect to

\mathrm{b}

f(b)=

\frac{b}{\sqrt{b^{2}+1}} \Rightarrow

f(x)=

\frac{x}{\sqrt{x^{2}+1}}

Practice Area Under Curves on Quantrex Academy →

More from Area Under Curves

The line y=m x bisects the area unclosed by lines x=0, y=0 and x=(3)/(2) and the curve… BITSAT 2024 If a, c, b are in GP, then the area of the triangle formed by the lines a x+b y+c=0 with… BITSAT 2024 The area enclosed by the curves y=x^3 and y= x is BITSAT 2024 The area of the region bounded by the curves x=y^2-2 and x=y is BITSAT 2024 If the area bounded by the curves y=a x^2 and x=a y^2,(a>0) is 3 sq units, then the value… BITSAT 2024 The area of the region R=\ (x, y): 5 x^2 ≤ y ≤ 2 x^2+9\ is : BITSAT 2023 The area enclosed between the curve y= _e(x+e) and the coordinate axes is BITSAT 2023 The area of the region bounded by the parabola (y-2)^2=(x-1) , the tangent to the… BITSAT 2022 The area enclosed by the curves y= x+ x and y=| x- x| over the interval [0, (π)/(2)] is BITSAT 2022 The area bounded by the curves x+2 y^ 2 =0 and x+3 y^ 2 =1 is BITSAT 2021 The area bounded by curves (x-1)^ 2 +y^ 2 =1 and x^ 2 +y^ 2 =1 is BITSAT 2021 The line y=m x bisects the area enclosed by lines x=0, y=0 and x=3 / 2 and the curve… BITSAT 2020 The point ( [ P + 1 ] , [ P ] ) (where, [ x ] is the greatest integer function) lying… BITSAT 2019 Area bounded by two branches of the curve (y - x)2 = x^ 3 and x = 1 is BITSAT 2019 The area of the region included between the curves x ^ 2 + y ^ 2 = a ^ 2 and |x| + |y| =… BITSAT 2018 The area under the curve y = | x - x|, 0 ≤ x ≤ (π)/(2) and above X -axis, is BITSAT 2017 Full Area Under Curves list Area Under Curves JEE Maths PYQs JEE Mathematics PYQs All BITSAT PYQs