Area of the region bounded by the x-axis and curves y-tanx-3- x -3 and y -cotx-6- x -3 -2 isA- log 2B- 2 log 2C- NoneD- log-2

The correct option is A log 2 y = tan x, y = cot x ⇒ tan x = cot x ⇒ x = π/4 Required area = ∫^π/4_0tanxdx+∫^π/4_π/4cotxdx = log | secx | ]^π/4_0+ log | sin ...

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Byju's Answer

Standard XII

Mathematics

Area between Two Curves

Area of the r...

Question

Area of the region bounded by the x-axis and curves $y = t a n x (\frac{- π}{3} \leq x \leq \frac{π}{3})$ and
$y = c o t x (\frac{π}{6} \leq x \leq \frac{3 π}{2})$ is

log 2

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2 log 2

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l o g \sqrt{2}

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None

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Solution

The correct option is A log 2

$y = t a n x, y = c o t x \Rightarrow t a n x = c o t x \Rightarrow x = \frac{π}{4}$
Required area = $\int_{0}^{\frac{π}{4}} t a n x d x + \int_{\frac{π}{4}}^{\frac{π}{4}} c o t x d x$
$= l o g | s e c x |]_{0}^{\frac{π}{4}} + l o g | s i n x |]_{\frac{π}{4}}^{\frac{π}{2}}$
$= l o g (\sqrt{2}) - 0 + 0 - l o g \frac{1}{\sqrt{2}} = l o g 2 s q . u n i t$

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Area of the region bounded by the x-axis and curves y=tanx(−π3≤x≤π3) and y=cotx(π6≤x≤3π2 ) is

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Area of the region bounded by the x-axis and curves $y = t a n x (\frac{- π}{3} \leq x \leq \frac{π}{3})$ and
$y = c o t x (\frac{π}{6} \leq x \leq \frac{3 π}{2})$ is