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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 : 193 of 271
Marks: +1, -0
∫0π(sin⁡2x2−cos⁡2x2)dx\int\limits_{0}^{\pi}\left(\frac{\sin^2 x}{2}-\frac{\cos^2 x}{2}\right)dx
Solution:  
∫0π(sin⁡2x2−cos⁡2x2)dx\int\limits_{0}^{\pi}\left(\frac{\sin^2 x}{2}-\frac{\cos^2 x}{2}\right)dx
=−∫0πcos⁡xdx=-\int\limits_{0}^{\pi}\cos x dx
=−[sin⁡x]0π=-\left[\sin x\right]^{\pi}_{0}
=−(sin⁡π−sin⁡0)=-(\sin\pi-\sin0)
=−(0−0)=0=-(0-0)=0
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