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Let $I = \int_{10}^{18} \frac{\cos x}{\sqrt{1 + x^{4}}} d x$
Statement-1: $| I | < 0.1$
Statement-2: $|\frac{\cos x}{\sqrt{1 + x^{4}}}| < 0.1$

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STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is a correct explanation for STATEMENT-1

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detailed solution

Correct option is B

Since cos⁡x≤1, the condition x>10 yields cos⁡x1+x4<10−2<10−1|I|<8.10−2<10−1.

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Let I=∫1018 cos⁡x1+x4dxStatement-1: |I|<0.1Statement-2: cos⁡x1+x4<0.1

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Let $I = \int_{10}^{18} \frac{\cos x}{\sqrt{1 + x^{4}}} d x$
Statement-1: $| I | < 0.1$
Statement-2: $|\frac{\cos x}{\sqrt{1 + x^{4}}}| < 0.1$