Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
NDA2024MathematicsIndefinite IntegrationActual

Paragraph: Let 2 x^2-1 x^2+1 d x= U (x) V (x)-3 U (x)+ V (x) +c Question: What is U (x) V (x) equal to?

Options

  1. Ax^2+x^4
  2. Bx+x^3
  3. Cx^2+x^4 2
  4. D2 x^2+x^4

Correct answer

D. 2 x^2+x^4

Step-by-step solution

aligned & I=2 x^2-1 x^2+1 d x=2 ( x^2+1 x^2+1 - 2 x^2+1 ) d x & =2 ( x^2+1 - 2 x^2+1 ) d x & =2 [ x 2 x^2+1 + 1 2 (x+ x^2+1 )-2 (x+ x^2+1 )+c . & =x x^2+1 + (x+ x^2+1 )-4 (x+ x^2+1 ) & =x x^2+1 -3 (x+ x^2+1 )+c & =U(x) V(x)-3 U(x)+V(x) +c & U(x)=x and V(x)= x^2+1 aligned U ( x ) V ( x )= x x ^2+1 = x ^4+ x ^2 = x ^2+ x ^4

Practice Indefinite Integration on Quantrex Academy →

More from Indefinite Integration

Passage: Let ,d (2+ )(3+4 ) =A |2+ |+B |3+4 | . Question: What is the value of A ? 2026Passage: Let ,d (2+ )(3+4 ) =A |2+ |+B |3+4 | . Question: What is the value of B ? 2026What is dx 10^x + 10^ -x equal to? 2025Consider the following for the two (02) items that follow: Let the function y = (1 - x)⁻¹ , where x 2n and n is an integer. What is y , dx equal to? 2025For the following two (02) items: Let u = e^x x , dx and v = e^x x , dx . Consider the following: I. du dx = -v II. dv dx = -u Which of the above is/are correct? 2025For the following two (02) items: Let u = e^x x , dx and v = e^x x , dx . What is u + v equal to? 2025Let d x x+1 - x-1 = (x+1)^ 3 2 + (x-1)^ 3 2 +c What is the value of ? 2024Paragraph: Let 2 x^2-1 x^2+1 d x= U (x) V (x)-3 U (x)+ V (x) +c Question: What is | U ^2(x)- V ^2(x) | equal to? 2024 Full Indefinite Integration list All NDA PYQs