Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
AP EAMCET202124 Aug 2021Morning ShiftMathematicsDefinite IntegrationActual

₀^ x x x+ x d x is equal to

Options

  1. A( -2) 2
  2. B+2 2
  3. C( +2) 2
  4. D-2 2

Correct answer

A. ( -2) 2

Step-by-step solution

₀^ x x x+ x d x Let I= ₀^ x x x+ x d x...(i) aligned _a^b f(x) d x & = _a^b f(a+b-x) d x I & = ₀^ ( -x) ( -x) ( -x)+ ( -x) d x I & = ₀^ ( -x)(- x) - x- x d x I & = ₀^ ( -x) x x+ x d x...(ii) aligned Adding Eqs. (i) and (ii), we get aligned 2 I & = ₀^ x x+( -x) x x+ x d x 2 I & = ₀^ x x+ x d x I & = 2 ₀^ x x+ x d x= 2 ₀^ x x 1 x + x x & = 2 ₀^ ( x 1+ x 1- x 1- x ) d x & = 2 ₀^ x(1- x) 1- ^2 x d x & = 2 ₀^ x- ^2 x ^2 x d x aligned aligned I= & 2 ₀^ ( x ^2 x - ^2 x ^2 x ) d x & 2 ₀^ ( x x- ^2 x ) d x & 2 ₀^ x x- ( ^2

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