First slide

Evaluation of definite integrals

Question

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

Moderate

A

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

STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is NOT a correct explanation for STATEMENT-1
C

STATEMENT-1 is True, STATEMENT-2 is False
D

STATEMENT-1 is False, STATEMENT-2 is True

Solution

Since $\cos x \leq 1$ , the condition $x > 10$ yields
$\begin{array}{l} |\frac{\cos x}{\sqrt{1 + x^{4}}}| < 10^{- 2} < 10^{- 1} \\ | I | < {8.10}^{- 2} < 10^{- 1} . \end{array}$

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