The area bounded by the curve, $y=-x^2$, x-axis, $x=1$ and $x=4$, is

The area bounded by the curve, $y=-x^2$, x-axis, $x=1$ and $x=4$, is
  1. 21 sq. units
  2. 10 sq. units
  3. 20 sq. units
  4. $\frac{21}{2}$ sq. units

Solution

$-\int_1^4\left(-x^2\right) \mathrm{d} x=\left[\frac{x^3}{3}\right]_1^4=\frac{64}{3}-\frac{1}{3}=21$ sq. units

Asked in: MHT CET 2022 (08 Aug Shift 1)

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