Start learning →

Indian Navy Pilot Definite Integrals — practice questions

Explore 1 free Definite Integrals questions in Indian Navy Pilot Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

Practise Definite Integrals with Quill →

Definite Integrals questions and exercises with answers

Showing questions 1–1 of 1.

$\displaystyle\int_0^{\pi/2} \log(\tan x)\, dx = ?$Read the answer and worked solution →

Worked practice questions

$\displaystyle\int_0^{\pi/2} \log(\tan x)\, dx = ?$

  1. $-(\pi/2)\ln 2$
  2. $0$ (by King's symmetry between $\sin$ and $\cos$)
  3. $\pi\ln 2$
  4. $\ln 2$
Show answer and solution

Correct answer: B. $0$ (by King's symmetry between $\sin$ and $\cos$)

$I = \int \log\tan x = \int(\log\sin x - \log\cos x)$. Both pieces equal by King's (previous problem), so the difference is 0.

Open this question →

How to practise

  1. Choose a Definite Integrals question and try to work out your answer.
  2. Open the question to check the correct answer and read its worked solution.
  3. Continue in the app for bite-sized lessons, explanations and review with Quill. You can start without creating an account.

More Mathematics topics

SequencesBinomial TheoremSequences and SeriesGeometryProbability & StatisticsVectors & 3D GeometryPermutations and CombinationsLinear Programming