Start Free Mock LoginAlready registered? Login here

Mathematics - Area Under Curves Question with Solution | TestHub

MathematicsArea Under CurvesArea bounded by two curvesMedium2 minPYQ_2019

MathematicsMediumsingle choice

The area of the region bounded by the curve $y = 2 x - x^{2}$ and the line $y = x$ is ________ square units.

Options:

Answer:

Solution:

Given curves $y = 2 x - x^{2}$ and $y = x$

$y = x$
$y = 2 x - x^{2}$
Points of intersection of curve
$y = 2 x - x^{2}$ and $y = x$ is $x = 0,$ and $x = 1$
Hence, required area $= \int_{0}^{1} (y_{1} - y_{2}) d x$
$\int_{0}^{1} [(2 x - x^{2}) - x] d x$
${(\frac{x^{2}}{2} - \frac{x^{3}}{3})}_{0}^{1} = \frac{1}{6}$ sq. unit

Stream:MHT_CETSubject:MathematicsTopic:Area Under CurvesSubtopic:Area bounded by two curves

⏱ 2mℹ️ Source: PYQ_2019

Doubts & Discussion

Loading discussions...