Quantrex 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(θ) = (4)/(3) (1 - ^6 θ - ^6 θ) , then _ n → ∞ (1)/(n) [...

If f(θ)=43(1−cos⁡6θ−sin⁡6θ)f(\theta) = \frac{4}{3} (1 - \cos^6 \theta - \sin^6 \theta), then lim⁡n→∞1n[f(1n)+f(2n)+f(3n)+⋯+f(nn)]=\lim_{n \to \infty} \frac{1}{n} \left[ \sqrt{f\left(\frac{1}{n}\right)} + \sqrt{f\left(\frac{2}{n}\right)} + \sqrt{f\left(\frac{3}{n}\right)} + \dots + \sqrt{f\left(\frac{n}{n}\right)} \right] =

Options

  1. A1−cos⁡12\frac{1 - \cos 1}{2}
  2. B1−cos⁡21 - \cos 2
  3. Csin⁡22\frac{\sin 2}{2}
  4. D1−cos⁡22\frac{1 - \cos 2}{2}

Correct answer

D. 1−cos⁡22\frac{1 - \cos 2}{2}

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 PYQsJEE Mathematics PYQs All Black Book Advanced Problems in Mathematics PYQs