JEE Main 2022 · 27 Jul · Shift 2 · Mathematics Q9

MathematicsSingle correct+4 / -1Question 9 of 90

$\displaystyle\int_0^2\left(\left|2x^2-3x\right|+\left[x-\frac12\right]\right)dx$ , where $[t]$ is the greatest integer function, is equal to :

\dfrac76

\dfrac{19}{12}

\dfrac{31}{12}

\dfrac32

Answer and worked solution

Official answer: B

Modulus part. $\int_0^{3/2}(3x-2x^2)dx=\frac98$ and $\int_{3/2}^2(2x^2-3x)dx=\frac{11}{24}$ .

Greatest-integer part. $-\frac12+0+\frac12=0$ .

Total $\frac{19}{12}$ . (B)

Topics:Properties of definite integrals

JEE Main 2022 · 27 Jul · Shift 2, Mathematics question 9