JEE Main 2015 · 11 Apr · Shift 1 · Mathematics Q75

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MathematicsSingle correct+4 / -1Question 75 of 90

Let $f:\mathbb R\to\mathbb R$ be a function such that $f(2-x)=f(2+x)$ and $f(4-x)=f(4+x)$ , for all $x\in\mathbb R$ and $\displaystyle\int_0^2f(x)\,dx=5$ . Then the value of $\displaystyle\int_{10}^{50}f(x)\,dx$ is :

100

125

200

Answer and worked solution

Official answer: B

Symmetry about $x=2$ and $x=4$ makes $f$ periodic with period 4. $\int_0^4f=2\times5=10$ , and $[10,50]$ covers 10 periods: $100$ .

Topics:Properties of definite integrals Types of functions

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JEE Main 2015 · 11 Apr · Shift 1, Mathematics question 75