-4-4 e x - 2 xdx - e 2 x-1 is equal toA- 2B- e C- 2 eD- 0

The correct option is D 0 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 ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Mathematics

Property 1

∫-π/4π/4 e x ...

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

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

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)

Suggest Corrections

Similar questions

\int_{- π / 4}^{π / 4} \frac{e^{x} \cdot {sec}^{2} x d x}{e^{2 x} - 1}

is equal to?

Q. If

I = \int_{\frac{- π}{4}}^{\frac{π}{4}} \frac{e^{sec x} | sin x | {sec}^{2} x d x}{(1 + e^{sin x})}

, then

I = \int \frac{1}{e^{2 x} + e^{- 2 x}} d x = \frac{A}{842} {tan}^{- 1} e^{2 x} + C

then A is equal to

\int_{- π / 4}^{π / 4} \frac{e^{x} {sec}^{2} x d x}{e^{2 x} - 1}

is equal to

The amplitude of $\frac{1}{i}$ is equal to

Join BYJU'S Learning Program

∫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