JEE Main 2022 · 29 Jun · Shift 1 · Mathematics Q17

← JEE Main 2022 · 29 Jun · Shift 1

MathematicsSingle correct+4 / -1Question 17 of 90

$\displaystyle\int_0^5\cos\left(\pi\left(x-\left[\frac x2\right]\right)\right)dx$ ,

where $[t]$ denotes greatest integer less than or equal to $t$ , is equal to :

-3

-2

Answer and worked solution

Official answer: D

Pieces. On $[0,2)$ the integrand is $\cos\pi x$ , on $[2,4)$ it is $\cos\pi(x-1)$ , on $[4,5]$ it is $\cos\pi(x-2)$ . Each whole period integrates to 0, and $\int_4^5\cos\pi x\,dx=0$ .

(D)

Topics:Properties of definite integrals

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JEE Main 2022 · 29 Jun · Shift 1, Mathematics question 17