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Explain solution RD Sharma class 12 chapter 19 Definite Integrals exercise Very short answer type question 45 maths

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Answer: \frac{\sqrt{2}-1}{\sqrt{2}}

Hint: you must know the rule of integration

Given: \int_{0}^{\frac{\pi}{4}} \sin \{x\} d x

Solution:  \int_{0}^{\frac{\pi}{4}} \sin \{x\} d x

\begin{aligned} &=-[\cos \{x\}]_{0}^{\frac{\pi}{4}} \\\\ &=-\left[\cos \frac{\pi}{4}-\cos 0\right] \end{aligned}

\begin{aligned} &=-\left[\frac{1}{\sqrt{2}}-1\right] \\\\ &=\frac{\sqrt{2}-1}{\sqrt{2}} \end{aligned}


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