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NCERT Class XII Mathematics Chapter - - Solutions

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Prove the following (Exercises 262 to 267)
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Question : 264 of 271
Marks: +1, -0
∫−11x17cos⁡4x dx=0\int\limits_{-1}^{1} x^{17} \cos^4 x \, dx = 0
Solution:  
Let I=∫−11x17cos⁡4x dxI = \int\limits_{-1}^{1} x^{17} \cos^4 x \, dx
Let f(x)=x17cos⁡4xf(x) = x^{17} \cos 4x
f(−x)=(−x)17cos⁡4(−x)f(-x) = (-x)^{17} \cos^4(-x) =−x17cos⁡4x=−f(x)= -x^{17} \cos^4 x = -f(x)
∴f(x)\therefore f(x) is an odd function, hence I=0I = 0
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