Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
AP EAMCET2009MathematicsDefinite Integration

₀^ 1 1+ x d x is equal to

Options

  1. A1
  2. B2
  3. C-1
  4. D-2

Correct answer

B. 2

Step-by-step solution

aligned & Let I= ₀^ 1 1+ x d x & = ₀^ 1 1+ 2 x 2 1+ ^2 x 2 d x & = ₀^ ^2 x 2 (1+ x 2 )^2 d x & Put x 2 =t 1 2 ^2 x 2 d x=d t & I= ₀^ 2 d t (1+t)^2 = [- 2 1+t ]₀^ =2 & aligned

Practice Definite Integration on Quantrex Academy →

More from Definite Integration

₀^1 2 x+5 x^2+3 x+2 ~d x= 2025₀^1 x^ 5 / 2 (1-x)^ 3 / 2 ~d x= 2025_ n [ 1 n^2 ^2 1 n^2 + 2 n^2 ^2 4 n^2 + 3 n^2 ^2 9 n^2 + + 1 n^2 ^2 1 ]= 2025₀^1 x Sin ⁻¹ x d x= 2025_ - 2 ^ 2 (x-[x]) d x= 2025₀^2 x^2(2-x)^5 d x= 2025If f(x)= Max x^3-4, x^4-4 , and g(x)= Min x^2, x^3 , then _ -1 ^1(f(x)-g(x)) d x= 2025_ n 2 n [ 2 n + 2 2 n + 3 2 n + + 2 ]= 2025 Full Definite Integration list All AP EAMCET PYQs