Test:351 QNo:44

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\int_{\pi /6}^{\pi /2}{log(sinx)cotxdx}

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6 Answers

1

Â°áƒ¦â€¢à¹“ÑÏ…Î ·2009-04-24 08:56:42

Q44 a) -(log2)2/4
b) -(log2)2 c) -(log2)2/2 d) -(log2)2/8

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1

Â°áƒ¦â€¢à¹“ÑÏ…Î ·2009-04-24 08:58:17

put losinx=t
so ur int bcums

t dt

so itz
t^2/2

so log sinx d whole squre /2

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11

Mani Pal Singh ·2009-04-24 08:59:13

integrate it by parts

Take the 1st function as log sinx and 2nd function as cot x

USE
âˆ«cotx=lnsinx

i hope u will get ur answer
if still doubt persists then ask again!!!!!!

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1357

Manish Shankar ·2009-04-24 09:23:53

(1/2)[(logsinx)²]_pi/6^pi/2=(1/2)[0-(log1/2)²]=-(log2)²/2

whats your doubt here

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1

Â°áƒ¦â€¢à¹“ÑÏ…Î ·2009-04-24 09:30:05

sirji answer c diye hai aapne

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1357

Manish Shankar ·2009-04-24 09:39:43

to (c) me to -(log2)²/2 yahi option diya ha na

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Your Answer

Basic Integral Calculus Operators Symbols Matrix Cases

√ √ || {} [] () → ~ ^ x x x → → ln log lg lim lim cos sin tan cot arcsin arccos arctan

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∑ ∑ ∑ ∑ ∑ ∮ ∮ ∮ ∮ ∮ ∏ ∏ ∏ ∏ ∏ ∐ ∐ ∐ ∐ ∐

+ - × ÷ ± ∓ = ∪ ∩ ≠ ∼ ≈ ∅ ∀ ∃ ∈ ∋ ∝ ≤ ≥ ≃ ≅ ≡ < > ≪ ≫ ⊂ ∉ ⊃ ⊆ ⊇ ⇒ ⇐ ⇔ ⇒ ⇐ ⇔ ⇑ ⇓ ⇕ → ← ↔ → ← ↔ ↑ ↓ ↕ ↖ ↗ ↘ ↙ ↪ ↩ ⇀ ↼ ⇁ ↽

° ∂ ∞ α β γ δ θ λ μ ν ξ π ρ σ φ ω ε ƒ κ τ υ Γ Δ Λ Σ Π Ω