The value of _(-3)^3 _e((4+x)/(4-x)) dx is Option 1: 2 Option 2: 0 Option 3: -1 Option 4: 3

Answer: 0. Solution: Let f(x) = ((4+x)/(4-x)). Then f(-x) = ((4-x)/(4+x)) = -f(x). So f is an odd function. Integral of an odd function over symmetric interval [-3, 3] equals 0.

Calculus

Integrals

Medium

The value of $\int_{-3}^{3} \log_e\left(\frac{4+x}{4-x}\right) dx$ is

-1

✅ Correct Option: 2

Let $f(x) = \log\left(\frac{4+x}{4-x}\right)$ . Then $f(-x) = \log\left(\frac{4-x}{4+x}\right) = -f(x)$ . So $f$ is an odd function. Integral of an odd function over symmetric interval $[-3, 3]$ equals 0.

2026: 29 May Shift 2

$\int \frac{1}{x(x^6+1)}\,dx =$ (consider $\log_e x = \log x$ )

2026: 18 May Shift 1

The value of $\int \frac{dx}{1+\sqrt{x}}$ is

2026: 14 May Shift 2

If C is an arbitrary constant, then

Match the LIST-I with LIST-II

	LIST-I		LIST-II
A.	$\displaystyle\int a^x \, dx$	I.	$\sin^{-1}\dfrac{x}{a} + C$
B.	$\displaystyle\int \dfrac{dx}{\sqrt{a^2 - x^2}}$	II.	$\log_e \vert x + \sqrt{x^2 - a^2} \vert + C$
C.	$\displaystyle\int \dfrac{dx}{\sqrt{a^2 + x^2}}$	III.	$\dfrac{a^x}{\log_e a} + C$
D.	$\displaystyle\int \dfrac{dx}{\sqrt{x^2 - a^2}}$	IV.	$\log_e \vert x + \sqrt{a^2 + x^2} \vert + C$

Choose the correct answer from the options given below:

2026: 21 May Shift 2

Let $[t]$ denotes the greatest integer $\le t$ , then the value of $\left[\displaystyle\int_{\pi}^{3\pi/2} x|\sin x|\,dx\right]$ is:

2026: 15 May Shift 1

If '[.]' is greatest integer function, then value of $\displaystyle\int_0^{1.5}[x^2]\,dx$ is equal to :

2022: 23 Aug Shift 1

$\int \sqrt{x^2 - 4x + 5} \, dx =$

The value of ∫−33log⁡e(4+x4−x)dx\int_{-3}^{3} \log_e\left(\frac{4+x}{4-x}\right) dx∫−33​loge​(4−x4+x​)dx is

Solution

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CUET Mathematics Past Year Questions (Topic-Wise)

The value of $\int_{-3}^{3} \log_e\left(\frac{4+x}{4-x}\right) dx$ is