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JEE Main · 2023 · 24 Jan 2023 · Shift 2 · Area Under Curves

The value of

12 \int_{0}^{3} x^{2} - 3 x + 2 dx

is

Answer: 22

Solution

Since

x^{2} - 3 x + 2 = (x - 1) (x - 2)

is positive on

[0, 1]

, negative on

[1, 2]

and positive on

[2, 3]

, split the integral at the roots. With antiderivative

\frac{x ^{3}}{3} - \frac{3 x ^{2}}{2} + 2 x

, the three contributions are

\int_{0}^{1} = \frac{5}{6}

,

\int_{1}^{2} = \frac{1}{6}

and

\int_{2}^{3} = \frac{5}{6}

, so

\int_{0}^{3} ∣ x^{2} - 3 x + 2∣ d x = \frac{11}{6}

. Multiplying by

12

gives

22.

JEE Main · 2023 · 24 Jan 2023 · Shift 2 · Integer answer

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