Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app

Black Advanced Problems in Mathematics

Exam: Black Advanced Problems in Mathematics
Subject: Mathematics
Chapter: Indefinite and Definite Integration

Black Advanced Problems in Mathematics · Mathematics · Indefinite and Definite Integration

If f(n) = (1)/(π) ∫_0^ π/2 ( ^2(nθ) dθ)/( ^2 θ), n ∈ N , then...

If

f(n) = \frac{1}{\pi} \int_0^{\pi/2} \frac{\sin^2(n\theta) d\theta}{\sin^2 \theta}, n \in N

, then evaluate

\frac{f(15) + f(3)}{f(12) - f(10)}

.

Correct answer

9

Step-by-step solution

Open this question in the Quantrex Academy app for the full interactive solution, figures and similar PYQs.

Practice Indefinite and Definite Integration on Quantrex Academy →

More from Indefinite and Definite Integration

**Paragraph for Question Nos. 1 to 2** Let f(x) = ∫ x^2 ^2 x (2x + 6 x - 2x ^2 x) dx and… Black Book Advanced Problems in Mathematics **Paragraph for Question Nos. 1 to 2** Let f(x) = ∫ x^2 ^2 x (2x + 6 x - 2x ^2 x) dx and… Black Book Advanced Problems in Mathematics **Paragraph for Question Nos. 3 to 4** Let f(x) be a twice differentiable function… Black Book Advanced Problems in Mathematics **Paragraph for Question Nos. 3 to 4** Let f(x) be a twice differentiable function… Black Book Advanced Problems in Mathematics **Paragraph for Question Nos. 3 to 4** Let f(x) be a twice differentiable function… Black Book Advanced Problems in Mathematics **Paragraph for Question Nos. 6 to 8** Consider the function f(x) and g(x) , both defined… Black Book Advanced Problems in Mathematics **Paragraph for Question Nos. 6 to 8** Consider the function f(x) and g(x) , both defined… Black Book Advanced Problems in Mathematics **Paragraph for Question Nos. 6 to 8** Consider the function f(x) and g(x) , both defined… Black Book Advanced Problems in Mathematics **Paragraph for Question Nos. 9 to 11** Let f(x) be function defined on such that f(1) =… Black Book Advanced Problems in Mathematics **Paragraph for Question Nos. 9 to 11** Let f(x) be function defined on such that f(1) =… Black Book Advanced Problems in Mathematics **Paragraph for Question Nos. 9 to 11** Let f(x) be function defined on such that f(1) =… Black Book Advanced Problems in Mathematics **Paragraph for Question Nos. 12 to 13** Let f_0(x) = x and for n ≥ 0 and x > 0 Let f_… Black Book Advanced Problems in Mathematics **Paragraph for Question Nos. 12 to 13** Let f_0(x) = x and for n ≥ 0 and x > 0 Let f_… Black Book Advanced Problems in Mathematics **Paragraph for Question Nos. 14 to 15** Let f : R arrow [-(3)/(4), ∞) be a surjective… Black Book Advanced Problems in Mathematics **Paragraph for Question Nos. 14 to 15** Let f : R arrow [-(3)/(4), ∞) be a surjective… Black Book Advanced Problems in Mathematics **Paragraph for Question Nos. 16 to 17** Let g(x) = x^c e^ cx and f(x) = ∫_0^x t e^ 2t (1… Black Book Advanced Problems in Mathematics Full Indefinite and Definite Integration list Indefinite and Definite Integration JEE Maths PYQs JEE Mathematics PYQs All Black Book Advanced Problems in Mathematics PYQs