int-pi -4-pi -2- Cotx-dx-2 log 2 logsqrt-2- log 2 displaystyle frac-pi-2- log2

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Toppr Admin · Accepted Answer

-x222B-x3C0-2-x3C0-4cotxdx-ln-sinx-x3C0-2-x3C0-4-ln-x2223-x2223-x2223-sin-x3C0-2-x2223-x2223-x2223-x2212-ln-x2223-x2223-x2223-sin-x3C0-4-x2223-x2223-x2223-ln-1-x2212-ln-1-x221A-2-0-x2212-x2212-log-x221A-2-log-x221A-2-

$\int_{π / 4}^{π / 2} C o t x . d x_{=}$

2 log 2
$log \sqrt{2}$
$log 2$
$\frac{π}{2}$ log2

$\int_{\frac{π}{4}}^{\frac{π}{2}} c o t x d x$

$= [l n | s i n x |]_{π / 4}^{π / 2}$

$= l n ∣ ∣ ∣ s i n (\frac{π}{2}) ∣ ∣ ∣ - l n ∣ ∣ ∣ s i n (\frac{π}{4}) ∣ ∣ ∣$

$= l n (1) - l n (\frac{1}{\sqrt{2}})$

$= 0 - (- l o g (\sqrt{2}))$

$= l o g (\sqrt{2})$ .

∫π/2π/4Cotx.dx=2 log 2 log√2 log2 π2 log2

∫π2π4cotxdx=[ln|sinx|]π/2π/4=ln∣∣∣sin(π2)∣∣∣−ln∣∣∣sin(π4)∣∣∣=ln(1)−ln(1√2)=0−(−log(√2))=log(√2).

$\int_{π / 4}^{π / 2} C o t x . d x_{=}$

2 log 2
$log \sqrt{2}$
$log 2$
$\frac{π}{2}$ log2

$\int_{\frac{π}{4}}^{\frac{π}{2}} c o t x d x$

$= [l n | s i n x |]_{π / 4}^{π / 2}$

$= l n ∣ ∣ ∣ s i n (\frac{π}{2}) ∣ ∣ ∣ - l n ∣ ∣ ∣ s i n (\frac{π}{4}) ∣ ∣ ∣$

$= l n (1) - l n (\frac{1}{\sqrt{2}})$

$= 0 - (- l o g (\sqrt{2}))$

$= l o g (\sqrt{2})$ .