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25 SELECTED QUES FOR JEE MAINS AND ADVANCED

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These questions are helpful for any exam u are preparing for

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INTEGRAL PROBLEMS 27P0, 27P1 18.08.2026
1. Find:

Ω= 𝑥 + 1+𝑥 𝑑𝑥, 𝑥 ∈ ℝ
2. If
(𝑥 + 1)
Ω= 𝑑𝑥 = 𝑢(𝑥 + 𝑒𝑥 + 𝑓𝑥 ) + 𝑄
11
𝑥 + 𝑥 + 11𝑥
3
5
Find 𝜗 = − (𝑎 + 𝑏 + 𝑐)
𝑘
3. Find
𝑥
Ω = lim 𝑑𝑥
→ (1 + 𝑥 )

4. Find
𝑥 cos 𝑥 + 𝑥 + sin 𝑥cos 𝑥
𝐼= 𝑑𝑥
𝑥sin 𝑥(𝑥 + cos 𝑥)
5. Find
cot 𝑥cot 2𝑥𝑑𝑥
Ω=
(cot 𝑥 − tan 𝑥)sin 2𝑥
6. Find
cos 2𝑥cot 𝑥𝑑𝑥 𝜋
Ω= , 𝑥 ∈ 0,
(cot 𝑥 − tan 𝑥)sin 2𝑥 4
7. Find

𝜋
Ω= tan(arccos(sin(arctan 𝑥)))𝑑𝑥, 0 < 𝑎 < 𝑏 <
2
8. Find
sin 3𝑥 ⋅ cos 𝑥 𝜋
Ω= 𝑑𝑥, 𝑥 ∈ 0,
cos 2𝑥 ⋅ cos 3𝑥 6

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