-4-4ex- sec2 x dx-e2x-1is equal to

Let I = ∫^π/4_ π/4e^x sec^2 x dx/e^2x 1 If f(x) = e^x sec^2 x/e^2x 1 If f(x) = e^x sec^2 x/e^2x 1 ∴ f ( x) = e^ x sec^2 x/e^ 2x 1 = e^x sec^2x/1 e^2x = ...

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Byju's Answer

Standard XIII

Mathematics

Property 1

∫π/4-π/4ex. s...

Question

$\int_{- \frac{π}{4}}^{\frac{π}{4}} \frac{e^{x} . s e c^{2} x d x}{e^{2 x} - 1}$ is equal to

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Solution

The correct option is A
0

Let $I = \int_{- \frac{π}{4}}^{\frac{π}{4}} \frac{e^{x} s e c^{2} x d x}{e^{2 x} - 1}$
If $f (x) = \frac{e^{x} s e c^{2} x}{e^{2 x} - 1} I f f (x) = \frac{e^{x} s e c^{2} x}{e^{2 x} - 1} ∴ f (- x) = \frac{e^{- x} s e c^{2} - x}{e^{- 2 x} - 1} = \frac{e^{x} s e c^{2} x}{1 - e^{2 x}} = - \frac{e^{x} s e c^{2} x}{e^{2 x} - 1} = - f (x) ∴ I = 0$
( f(x) is odd function)

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∫π4−π4ex.sec2xdxe2x−1is equal to

The correct option is A 0 Let I=∫π4−π4exsec2xdxe2x−1 If f(x)=exsec2xe2x−1If f(x)=exsec2xe2x−1∴f(−x)=e−xsec2−xe−2x−1=exsec2x1−e2x=−exsec2xe2x−1=−f(x)∴I=0 ( f(x) is odd function)

$\int_{- \frac{π}{4}}^{\frac{π}{4}} \frac{e^{x} . s e c^{2} x d x}{e^{2 x} - 1}$ is equal to