JEE Main 2022 · 25 Jul · Shift 2 · Mathematics Q9

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MathematicsSingle correct+4 / -1Question 9 of 90

Let $[t]$ denote the greatest integer less than or equal to $t$ . Then the value of the integral $\displaystyle\int_{-3}^{101}\left([\sin(\pi x)]+e^{[\cos(2\pi x)]}\right)dx$ is equal to

\dfrac{52(1-e)}e

\dfrac{52}e

\dfrac{52(2+e)}e

\dfrac{104}e

Answer and worked solution

Official answer: B

Period 2 for $[\sin\pi x]$ (integral $-1$ per period) and period 1 for $e^{[\cos2\pi x]}$ (value 1 on half the period, $e^{-1}$ on the other half).

Over 104 units. $-52+104\cdot\frac12(1+e^{-1})=\frac{52}e$ .

(B)

Topics:Properties of definite integrals

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JEE Main 2022 · 25 Jul · Shift 2, Mathematics question 9