Question
Download Solution PDF\(\rm \int_{-\pi/2}^{\pi/2} sin^9x\ dx\) का मान ज्ञात करें।
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFअवधारणा:
एक फलन f(x) विषम है यदि f(-x) = - f(x) और फलन सम है यदि f(-x) = f(x)
यदि फलन सम या विषम है और अंतराल [-a, a] है तो हम इन नियमों को लागू कर सकते हैं:
जब f(x) सम है:
\(\rm \int_{-a}^{a} f(x)\ dx = 2\int_{0}^{a} f(x)\ dx\)
जब f(x) विषम है:
\(\rm \int_{-a}^{a} f(x)\ dx =0\)
गणना:
दिया गया फलन है, f(x) = sin9x
f(-x) = sin9(-x)
= - sin9x
= - f(x)
चूंकि फलन विषम है \(\rm \int_{-\pi/2}^{\pi/2} sin^9x\ dx\) = 0
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