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NCERT Class XII Mathematics Chapter - - Solutions

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Exercise - 7.9
Evaluate the definite integrals in Exercises 176 to 195.
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Question : 179 of 271
Marks: +1, -0
∫0π/4sin⁡2xdx\int\limits_{0}^{\pi/4}\sin 2x dx
Solution:  
∫0π/4sin⁡2xdx\int\limits_{0}^{\pi/4}\sin 2x dx
=[−12cos⁡2x]0π/4=\left[-\frac{1}{2}\cos 2x\right]_{0}^{\pi/4}
=−12(cos⁡π2−cos⁡0)=-\frac{1}{2}\left(\cos \frac{\pi}{2} - \cos 0\right)
=−12(−1)=12=-\frac{1}{2}(-1)=\frac{1}{2}
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