CUET Mathematics - The value of _1^3 x^2/x^3+1dx | PYQs + Solutions

CUET Mathematics 2025 21 May Shift 2

Calculus

Medium

common

$\frac{1}{3}\log 26$

$\log 14$

$\frac{1}{3}\log 14$

$\log 56$

✅ Correct Option: 3

Related questions:

21 May Shift 1

Match List-I with List-II (Given that $c$ is an arbitrary constant)

List-I	List-II
(A) $\int \frac{dx}{\sqrt{a^2 - x^2}} =$	(I) $\log_e \|x + \sqrt{x^2 - a^2}\| + c$
(B) $\int \sqrt{a^2 - x^2} dx =$	(II) $\sin^{-1} \frac{x}{a} + c$
(C) $\int \sqrt{x^2 - a^2} dx =$	(III) $\frac{x}{2} \sqrt{a^2 - x^2} + \frac{a^2}{2} \sin^{-1} \frac{x}{a} + c$
(D) $\int \frac{dx}{\sqrt{x^2 - a^2}} =$	(IV) $\frac{x}{2} \sqrt{x^2 - a^2} - \frac{a^2}{2} \log_e \|x + \sqrt{x^2 - a^2}\| + c$

Choose the correct answer from the options given below:

26 May Shift 2

If $f(x)$ and $g(x)$ are continuous functions in [0, a] such that $f(x) = f(a - x)$ and $g(x) + g(a - x) = a$ then $\int_{0}^{a} f(x)g(x)dx =$

2 June Shift 1

The value of $\int_0^1 \log_e\left(\frac{1}{x} - 1\right)dx$ is:

CUET Mathematics 2025 21 May Shift 2 PYQs