Q5 / 116 · NTA Abhyas (JEE Main) 2020 · Mathematics · Definite Integration

Consider $I = \int_{0}^{1} \frac{d x}{1 + x^{5}}$ . Then, $I$ satisfies

A
$I > 1$
B
$I = 1$
Correct answer
C
$I < 1$
D
$I + 1 < 0$

Solution

As,

x \in (0, 1)

x^{5} \in (0, 1)

∴ 1 + x^{5} \in (1, 2)

\Rightarrow 1 + x^{5} > 1

∴ \int_{0}^{1} \frac{d x}{1 + x^{5}} < \int_{0}^{1} 1 d x

\Rightarrow I < 1

Hence, the correct answer is option: 'C'.

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