The value of _(-/3)^(/3)1/(1+e^( x))dx is: Option 1: /3 Option 2: -/3 Option 3: (2)/3 Option 4: ()/6

Answer: /3. Solution: With f(x)=1/(1+e^( x)), we get f(x)+f(-x)=1. Adding I to itself using the king property, 2I=_(-/3)^(/3)1 dx=(2)/3, so I=()/3.

Calculus

Integrals

Medium

core

The value of $\int_{-\pi/3}^{\pi/3}\frac{1}{1+e^{\tan x}}dx$ is:

$\pi/3$

$-\pi/3$

$\frac{2\pi}{3}$

$\frac{\pi}{6}$

✅ Correct Option: 1

With $f(x)=\frac{1}{1+e^{\tan x}}$ , we get $f(x)+f(-x)=1$ . Adding $I$ to itself using the king property, $2I=\int_{-\pi/3}^{\pi/3}1\,dx=\frac{2\pi}{3}$ , so $I=\frac{\pi}{3}$ .

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$\int_1^{\sqrt{3}} \frac{1}{1+x^2} dx$ is equal to:

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$\int_{-1}^{1}(x^7 + x^5 + x^3 + x + 1)dx$ is equal to

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$\int e^{2x}(\sin x + \frac{1}{2}\cos x) dx$ is equal to

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Value of $\displaystyle\int_{-1}^{1} \dfrac{x^5+|x|+1}{x^2+2|x|+1}\,dx$ is equal to :

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The integral $\int e^x \left(\frac{x-1}{2x^2}\right) dx$ is equal to:

The value of ∫−π/3π/311+etan⁡xdx\int_{-\pi/3}^{\pi/3}\frac{1}{1+e^{\tan x}}dx∫−π/3π/3​1+etanx1​dx is:

Solution

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CUET Mathematics Past Year Questions (Topic-Wise)

The value of $\int_{-\pi/3}^{\pi/3}\frac{1}{1+e^{\tan x}}dx$ is: