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NTA Abhyas 2020
Exam
NTA Abhyas
Year
2020
Subject
Mathematics
Chapter
Indefinite Integration

NTA Abhyas 2020 · Mathematics · Indefinite Integration

The value of ∫ 1 (2x - 1) x^ 2 - x dx is equal to (where c & is the...

The value of ∫1(2x−1)x2−xdx∫ \dfrac{1}{\left(2x - 1\right)\sqrt{x^{2} - x}}dx is equal to (where cc& is the constant of integration)

Options

  1. Asec−1(x−1)+csec^{- 1}\left(x - 1\right) + c
  2. Bsec−1(2x−1)+csec^{- 1}\left(2x - 1\right) + c
  3. Ctan−1x+ctan^{- 1}x + c
  4. Dtan−1(2x−1)+ctan^{- 1}\left(2x - 1\right) + c

Correct answer

B. sec−1(2x−1)+csec^{- 1}\left(2x - 1\right) + c

Step-by-step solution

∫2(2x−1)4x2−4xdx=2∫dx(2x−1)(2x−1)2−1∫ \dfrac{2}{\left(2x - 1\right)\sqrt{4x^{2} - 4x}}dx = 2∫ \dfrac{dx}{\left(2x - 1\right)\sqrt{{\left(2x - 1\right)}^{2} - 1}}

=2×12sec−1(2x−1)+c= 2 \times \dfrac{1}{2}sec^{- 1}\left(2x - 1\right) + c
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