Let f be a polynomial function such that f ( x 2 +1 )= x 4 +5 x 2 +2 ，for all x in mathbb R ． Then int 0 3 f( x ) dx is equal to

Mathematics · Definite Integration

JEE Main 2026 — 28 January, Morning Shift — Question 11

Let $f$ be a polynomial function such that $f\left(\mathrm{x}^{2}+1\right)=\mathrm{x}^{4}+5 \mathrm{x}^{2}+2$ ，for all $\mathrm{x} \in \mathbb{R}$ ． Then $\int_{0}^{3} f(\mathrm{x}) \mathrm{dx}$ is equal to

Option A:
$\frac{41}{3}$
Option B:
$\frac{33}{2}$
Correct
Option C:
$\frac{27}{2}$
Option D:
$\frac{5}{3}$

Answer: B

Step-by-step solution

Now， $\int_{0}^{3} f(t) d t=\int_{0}^{3}\left(t^{2}+3 t-2\right) d t$

$\left[\frac{\mathrm{t}^{3}}{3}+\frac{3 \mathrm{t}^{2}}{2}-2 \mathrm{t}\right]_{0}^{3}$

$\left[\frac{27}{3}+\frac{27}{2}-6\right]$

$=\frac{33}{2}$

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Exam: JEE Main 2026
Paper: 28 January, Morning Shift
Subject: Mathematics
Chapter: Definite Integration
Topic: Evaluation of Definite Integrals

The value of sum r=1^20 ( sqrtpi (int 0^ r x sin pi x dx ) ) is \ \ \ \ .

Answer: B

Step-by-step solution

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