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Application of Integration question

2023 · Shift 1 · Q26

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PYQ Library
JEE Advanced
Mathematics
Application of Integration
2023 · Shift 1 · Q26

Application of Integration question

2023 · Shift 1 · Q26

JEE AdvancedMathematicsApplication of IntegrationNumerical+4 / −1

Let

n \geq 2

be a natural number and

f:[0,1] \rightarrow \mathbb{R}

be the function defined by

f(x)= \begin{cases}n(1-2 n x) & \text { if } 0 \leq x \leq \frac{1}{2 n} \\\\ 2 n(2 n x-1) & \text { if } \frac{1}{2 n} \leq x \leq \frac{3}{4 n} \\\\ 4 n(1-n x) & \text { if } \frac{3}{4 n} \leq x \leq \frac{1}{n} \\\\ \frac{n}{n-1}(n x-1) & \text { if } \frac{1}{n} \leq x \leq 1\end{cases}

If

n

is such that the area of the region bounded by the curves

x=0, x=1, y=0

and

y=f(x)

is 4 , then the maximum value of the function

f

is :

Numerical answer

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