Q.1 (vi) If ∫_(-π/4)^(π/4) x³ · sin⁴ x dx = k then k = _____. A. 1 B. 2 C. 4 D. 0

Answer: D. 0 Answer: (d) 0 Let f(x) = x³ sin⁴ x . Then f(-x) = (-x)³ (sin(-x))⁴ = -x³ sin⁴ x = -f(x) , so f is an odd function. For an odd function, ∫_(-a)^a f(x) dx = 0 . Hence k = 0 .

If \(\int_{-\pi/4}^{\pi/4} x^3 \cdot \sin^4 x \, dx = k\) then \(k =\) _____.

Q.1 (vi) If \(\int_{-\pi/4}^{\pi/4} x^3 \cdot \sin^4 x \, dx = k\) then \(k =\) _____.

A. 1

B. 2

C. 4

D. 0

Doubtly Asked 29 Oct 2026 Board exam · March 2024 hsc 12th Save WhatsApp Report

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Answer: D. 0

Answer: (d) 0

Let \(f(x) = x^3 \sin^4 x\). Then \(f(-x) = (-x)^3 (\sin(-x))^4 = -x^3 \sin^4 x = -f(x)\), so \(f\) is an odd function. For an odd function, \(\int_{-a}^{a} f(x)\,dx = 0\). Hence \(k = 0\).

Doubtly AI · 29 Oct 2026 AI-generated · not yet verified Report

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If \(\int_{-\pi/4}^{\pi/4} x^3 \cdot \sin^4 x \, dx = k\) then \(k =\) _____.

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