Evaluate the definite integrals- -6-4cosec x d x

I =∫_π/6^π/4cosec x dx =[log |cosec x cot x|]^π/4_π/6 =log | cosec π/4 cot π/4 | log | cosec π/6 cot π/6 | =log |√(2) 1| log |2 √(3)|=log | √(2) 1/2 √(3) | ...

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Standard XII

Mathematics

Factorization Method Form to Remove Indeterminate Form

Evaluate the ...

Question

Evaluate the definite integrals.
$\int_{\frac{π}{6}}^{\frac{π}{4}} c o s e c x d x .$

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Solution

$I = \int_{\frac{π}{6}}^{\frac{π}{4}} c o s e c x d x = [l o g | c o s e c x - c o t x |]_{\frac{π}{6}}^{\frac{π}{4}} = l o g ∣ ∣ c o s e c \frac{π}{4} - c o t \frac{π}{4} ∣ ∣ - l o g ∣ ∣ c o s e c \frac{π}{6} - c o t \frac{π}{6} ∣ ∣ = l o g | \sqrt{2} - 1 | - l o g | 2 - \sqrt{3} | = l o g ∣ ∣ ∣ \frac{\sqrt{2} - 1}{2 - \sqrt{3}} ∣ ∣ ∣ (∵ l o g a - l o g b = l o g \frac{a}{b})$

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Evaluate the definite integrals. ∫π4π6cosecxdx.

I=∫π4π6cosecxdx=[log|cosecx−cotx|]π4π6=log∣∣cosecπ4−cotπ4∣∣−log∣∣cosecπ6−cotπ6∣∣=log|√2−1|−log|2−√3|=log∣∣∣√2−12−√3∣∣∣(∵loga−logb=logab)

Evaluate the definite integrals.
$\int_{\frac{π}{6}}^{\frac{π}{4}} c o s e c x d x .$