Evaluate using Trigonometric Identities MCQ Quiz in বাংলা - Objective Question with Answer for Evaluate using Trigonometric Identities - বিনামূল্যে ডাউনলোড করুন [PDF]
Last updated on Apr 29, 2025
Latest Evaluate using Trigonometric Identities MCQ Objective Questions
Evaluate using Trigonometric Identities Question 1:
\(\rm \int_0^{2\pi}\theta sin ^6 \theta\cos \theta d\theta\)-এর মান হল
Answer (Detailed Solution Below)
Evaluate using Trigonometric Identities Question 1 Detailed Solution
Evaluate using Trigonometric Identities Question 2:
যেকোনো পূর্ণসংখ্যা n-এর জন্য, \(\int_{0}^{\pi} \mathrm{e}^{\cos ^{2} x} \cdot \cos ^{3}(2 n+1) x \mathrm{~d} x\) এর মান কত?
Answer (Detailed Solution Below)
Evaluate using Trigonometric Identities Question 2 Detailed Solution
গণনা:
প্রদত্ত, I = \(\int_{0}^{\pi} \mathrm{e}^{\cos ^{2} x} \cdot \cos ^{3}(2 n+1) x \mathrm{~d} x\) … (i)
⇒ \(\int_{0}^{\pi} \mathrm{e}^{\cos ^{2} (\pi-x)} \cdot \cos ^{3}[(2 n+1) (\pi-x)] \mathrm{~d} x\)
⇒ \(\int_{0}^{\pi} \mathrm{e}^{\cos ^{2} x} \cdot \cos ^{3}[(2 n+1)\pi-(2n+1)x] \mathrm{~d} x\)
⇒ \(-\int_{0}^{\pi} \mathrm{e}^{\cos ^{2} x} \cdot \cos ^{3}(2 n+1) x \mathrm{~d} x\) … (ii)
(i) এবং (ii) যোগ করে পাই:
⇒ 2I = 0
⇒ I = 0
∴ যেকোনো পূর্ণসংখ্যা n-এর জন্য সমাকলের মান 0।
সঠিক উত্তর বিকল্প 3.
Top Evaluate using Trigonometric Identities MCQ Objective Questions
Evaluate using Trigonometric Identities Question 3:
\(\rm \int_0^{2\pi}\theta sin ^6 \theta\cos \theta d\theta\)-এর মান হল
Answer (Detailed Solution Below)
Evaluate using Trigonometric Identities Question 3 Detailed Solution
Evaluate using Trigonometric Identities Question 4:
যেকোনো পূর্ণসংখ্যা n-এর জন্য, \(\int_{0}^{\pi} \mathrm{e}^{\cos ^{2} x} \cdot \cos ^{3}(2 n+1) x \mathrm{~d} x\) এর মান কত?
Answer (Detailed Solution Below)
Evaluate using Trigonometric Identities Question 4 Detailed Solution
গণনা:
প্রদত্ত, I = \(\int_{0}^{\pi} \mathrm{e}^{\cos ^{2} x} \cdot \cos ^{3}(2 n+1) x \mathrm{~d} x\) … (i)
⇒ \(\int_{0}^{\pi} \mathrm{e}^{\cos ^{2} (\pi-x)} \cdot \cos ^{3}[(2 n+1) (\pi-x)] \mathrm{~d} x\)
⇒ \(\int_{0}^{\pi} \mathrm{e}^{\cos ^{2} x} \cdot \cos ^{3}[(2 n+1)\pi-(2n+1)x] \mathrm{~d} x\)
⇒ \(-\int_{0}^{\pi} \mathrm{e}^{\cos ^{2} x} \cdot \cos ^{3}(2 n+1) x \mathrm{~d} x\) … (ii)
(i) এবং (ii) যোগ করে পাই:
⇒ 2I = 0
⇒ I = 0
∴ যেকোনো পূর্ণসংখ্যা n-এর জন্য সমাকলের মান 0।
সঠিক উত্তর বিকল্প 3.